Hi David,
I have to disagree with Dmitrii a bit here.
I would say the answer to your question depends on the size of your site and how many articles and tags you are talking about - on bigger sites with more tags, they can become quite an issue.
On a big-ish news site that I own and run (14,000+ articles), I added "noindex" to all tag pages (2,000+) and then blocked them in robots.txt a few months later (once Google had crawled and removed them all from index).
The reason for removing and blocking them for search engines is that tag pages generally don't offer anything unique or of substantial value when compared to other pages on your site site, and they can also use up a lot of your "crawl budget".
For the site mentioned, I saw around a 30% organic traffic increase after implementing these changes.
The tags are still there for users, but they are not visible to search engines and means that search engines are now only crawling pages that we want indexed and ranking, instead of wasting their time crawling thousands of links to thousands of tag pages.
Basically, don't think of tags as a way to "help your SEO" because they probably won't and they have the potential to do the opposite.
If you think creating a particular tag will help you get long-tail traffic, write an article about that topic instead! I guarantee you it will perform a lot better than a tag page.
Cheers,
David