For example, consider a page that ranks well organically and receives (relatively) decent traffic from search. However, this page has poor engagement metrics compared to other pages on the site, does not convert visitors as well as other pages on the site, and doesn't have any external links. Would you consider deleting this page?

I would improve the page.

Beef up the content, add seductive links to get traffic to a more valuable page, add adsense to earn money if the traffic is low quality.

Which metrics do you use when auditing a site and considering a web page from removal (bounce rate, average time on site, pages per visit, linking root domains, visits, revenue per visit, etc.)?

If someone brought me a site that needed help I would do keyword research to determine if they are covering the important queries for their line of business.  If they are not I would have a content plan to get them covered.  If they are covered but performing poorly we would improve those pages.

Looking at the numbers you suggest is like cutting off a foot because you have a blister on your toe.  Decide instead if the foot is valuable.  If yes, cure it.

The most likely negative result is that Google will know that the links are paid and they will pass no value - thus wasted money.

Another potential negative result is that these links will stink up your link profile and your rankings will suffer.  Nobody knows exactly how google detects of measures this.

If you have a great site stay on the white hat path.... if the only way you can get links is by shady methods... guess you are stuck with them.

There is something called "link rot"... that every site experiences.  You earn some links a long time ago and most of those links will eventually disappear for reasons described by effectdigital.    If your new content production pace is not as fast as in the past, then you can be losing more links than you are earning.   Link rot hits sites that are slacking on their content production.

And, as Mr Whippy said...  "The domain linking to you is clearing out links that point to your content as they feel there is better content to link to now."    Sometimes competitors will see your content, produce something much better, then solicit the linking websites to link to their content that is now much better than yours.   We receive lots of emails suggesting better destinations for links in existing articles.   These email messages can be valuable to a webmaster, but if we look at their suggested content and it is crap, we filter their email address to trash.

PDFs can be canonicalized using .htaccess.  Google is usually very slow to discover and obey this but it can be done.  However, if your PDF is not close to being an exact copy of the target page, Google will probably not honor the canonicalization and they will index the PDF and the html page separately.

https://www.inmotionhosting.com/support/website/how-to-canonicalize-images-and-pdfs-with-the-htaccess-file

PDFs can be optimized (given a title tag) by editing the properties of the document.  Most PDF - making software has the ability to do this.

You can insert "buy buttons" and advertising in PDFs.  Just make an image, paste it into the document and link it to your shopping cart or to your target document.

PDFs accumulate linkjuice and pass it to other documents.

Use the same strategies with PDFs as you would with an html page for directing visitors where you want them to go and getting them to do what you want them to do.

Some people will link to your PDF, others will grab your PDF and place it on their website (in that situation, you lose the canonical but still get juice from any embeded links), and benefit from ads and buttons that might be included.  Lock the PFD with your PDF-creating software to prevent people from editing your PDF (but they can always copy/paste to get around it).

Other types of documents such as Excel spreadsheets, PowerPoint documents, Google images, etc can have embedded text, embedded links and other features that are close to equivalent to an html document.

First, I am surprised that the CTR is so low because of your top ranking.  My goal with that would be to change the title tag and description tag to match the query as closely as possible and to elicit clicks.

If this was my site I would change the title tag to match the query.... and to elicit clicks.

I don't know your business so I am going to guess.

<title>Granite Countertops: Prompt Installation in St. Louis area</title>

They will see the name of your business in your domain.

Then I would change the description tag.   Study the adwords guys.  They have great descriptions...

Over 100 colors,  Fast, expert installation, Affordable countertops and replacements.  Tell them what they are looking for that you can deliver.

Google doesn't reveal exactly how this works.  However there are more than one benefit from a link.

First you have anchor text value.  That would be noted and credited to the page.

Next you have PageRank.  That would flow into a page but most of that PageRank (about 85% according to the original pagerank theory) would flow out through links in that page.  Those receiving pages would pass PageRank on to the pages that they link to... and this process would continue over and over and over.  Some of those pages downstream would link back to the original page that received the link and strength of that page would build by small amounts as the calculation for each linkage step is done.  It is very unlikely that all of these calculations are done immediately.

Other variables might also count.  Such as a "trust" value for the linking domain or a value for topical relevance.

Most of us have seen a page that received a nice link move up in the SERPs a few days later.  But I highly doubt that all of the benefit is immediately received.  There are too many calculations involved and Google might do some of them quickly but others might be done in batch jobs at some future time.

I vote for the one big site.

Which will rank better?  One big site with 300 links or three little sites with 100 links each?  My money is on the big site.

Which will be more linkable?  One big site with a cluster of products or three hotdog stands with one product each?

Which will give you the opportunity of cross-selling and larger, more profitable sales?  A big site with multiple products or three tiny sites with one product each?

Which will be more work and expense to run?

I used to have a cluster of little sites and then combined them into one big site... and that big site beat all of the smaller sites and all of their competitors.

This company might believe that the work that they do is proprietary.  They don't want you to sniff it because they worry that you will discover valuable information that will enable you to leave them and benefit from their work.

If you sell products or services that are common and leave them, there is a good chance that they will take what they learned from you and offer similar service to another business, or set up their own business - if they are not doing it already.  This depends upon them being prevented to doing that by confidentiality language in your contract.  Otherwise it might be considered as their proprietary data.

If I was in your situation, I would examine my contract with this company and see if there is anything in there that prevents me  from visiting the account to verify that they are spending what they say they are spending and that I am the beneficiary of the entire spend.

I am not an attorney but I am pretty sure that there is nothing criminal about their arrangement with you.  But, you have no way of knowing what's happening deep down without full access to the account and all of its historical record.   You probably don't have any civil claim against them unless you can prove that they are violating a contract that both of you have signed.  This is certainly where an attorney would be helpful, if the service provider is located where enforcement is possible.  Otherwise, you will probably have to wait until your contract is up for renewal or negotiate a termination.

Based upon my own use of Adwords, I believe that things work best when bidding strategies are informed by pricing, costs of good sold, profit margins, and lifetime customer values..... and pricing strategies at the item level can't be wisely set if you only have aggregated data.  That would be my argument to get access to the account.  Bidding and selling are best done with shared data rather than things being held secret... but some people have a poor understanding of that or simply want to work behind a curtain without knowing if they are delivering best possible performance.  That's personal opinion.