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Glad you figured it out. I honestly didn't think it would have been the canonicals. I'm a little surprised that the bots didn't just choose not to respect the suggestion as opposed to blanking your site from the index. Didn't think that was even a possibility from incorrect canonicals. Good to know for the future though in case anything like this comes up with anyone else's site.

Not exactly. Its not so much that the canonical "supersedes" an index, follow tag.... a canonical tag establishes equivalency while a NoIndex is more like a "does not equal." The Index, Follow is still there and being seen by bots as they crawl... in fact, if you had NoIndex on a page with a Canonical Tag, it may not even see the canonical at all since you told it to NoIndex the page. The Meta Robots Index tag comes first allowing the bots to crawl and index the page but then the canonical sets up equivalency to a separate page. So if your canonical tag is being respected, it doesn't wind up doing the same thing as a NoIndex (though it may seem that way) nor does it do the same thing as a 301 (though there are similarities in how equity is passed). Since a canonical establishes an equivalency, you'll find that the Canon Page will eventually take the place of the Canonicalized Page in search results because you're telling them the Canonicalized Page _is _the Canon Page & that the Canon page is the right version of both.

I took a look at all of the usual suspects as well... which amounts to pretty much everything that everyone else mentioned but I was intrigued by this issue and thought maybe another set of eyes might notice something that was off. Nothing was wrong in the page source from what I saw, no issues crawling it myself and I didn't see any penalties. Normally I'd think that if your homepage wasn't appearing for branded organic searches then a penalty was levied against you but when that is the case the homepage is still normally find-able in a Site operator search. M__aybe it is related to all the backlinks that were lost/deleted in the past month but I'm not sure why that would be the case unless removing the homepage from the index was a Penguin response to link issues... but I was under the impression that peguin was devaluing the link source not the link recipient and deleting/removing links seems to be a preferred method of handling penguin-related issues. So if there is a relationship between penguin and your homepage being deindexed then I am not sure at all why nor am I certain how to fix it as I'm not seeing anything in particular that screams "linking issue" at me. (though I only did a fairly cursory inspection of things)

So I am stumped. Whenever the issue is figure out I would love to know how/why this came to be.

If a URL was indexed and has since had a canonical added to it pointing to another page, it will eventually disappear from results. Basically the pages gets consolidated with its canon page. If the bots choose to respect the canonical tag in that instance, all signals get passed to the canon page while still allowing the page and information to be accessible by human visitors. As such, there's no reason to keep the page in the index because you're telling the bots that another page is the correct page instead. This is not the same as NoIndexing a page but will eventually remove a page from the index much in the same way that a 301 will pass equity along to another page while eventually removing the redirected page from the index in favor of the page being redirected to.

It is absolutely natural for people to link to your website with your URL. When looking at your backlink profile, you should see tons of links with the anchor text being things like your naked url or "website" or "this". In fact, it would be incredibly unnatural, and potentially a sign of paid linking schemes, if every single link to your website was a keyword rich, long tail anchor.

There is nothing "bad practices" about allowing a non-existent page to 404. People often times forget that a 404 isn't a signal that something is broken and needs fixing, its just a status code that returns "Not Found". Sometimes it makes sense for things not to be found on your site because they were never there in the first place. 404s eventually stop being crawled and indexed.

You shouldn't just bulk redirect things to your homepage though. Its always best to have a 301 point to the most relevant page based on what the original page was. If there is no most relevant page, have you considered 301-ing them to one step up in the site navigation? (i.e. a category page or hub page)