Tags serve no purpose. Neither does the Dewey Decimal Classification system or the Library of Congress Classification system serve any purpose in libraries. For that matter, directories in hard drive file systems are just a waste of space on the drive. After all, every question has a title, just like every book does, and every file has a name. I can search for the title I want when looking for a question, and I can see from the title what it's about without needing to look at the tags.
Having said that, as a tongue-in-cheek reply to your tongue-in-cheek question, lets look at a few of the purposes truly served, and how it falls apart.
- Notices: I can subscribe to an RSS feed for a tag such as apache and get notified of question activity for that tag. If I'm an expert in that area and wish to share my knowledge with others, this will let me know when others have questions that might benefit from that knowledge.
- This presupposes that the tag is applied to questions where it should be, and only where it should be. I will miss questions that might qualify if the tag isn't applied to the question.
- Suffers from "false positives" when a question has a tag it doesn't deserve, or need, as noted with examples in the answer from @Arminius. This puts questions in the feed that don't belong there, and require you to filter them out yourself.
- As pointed out by @schroeder in his answer, I can highlight or dim questions in the listings based on my preferences using tags. Again this helps find what I have an interest in, and ignore what I have no interest in, and keeps everything else "open for investigation" in the list. (I'd rather it eliminated, rather than dimmed, the ignored tags.)
- It is also possible to list questions that only have a tag applied to them, ignoring all others. Handy if I have a question about something, but don't know how to ask it.
- Both of these suffer from tags not being applied when they should have been like Notices above. Unless they have one of the ignored tags, however, I will still see them, just not highlighted.
- Again, both of these are affected by false positives.
- Association: As noted by @Anders in his answer, tags help the system connect one question to others that are related. When looking for answers to a question, this can be very helpful. When answering a question it can also alert you to similar questions that might have useful information to link to, or otherwise include, in your answer.
- This is affected more by having wrong tags on questions than by not having enough of the right tags, when you are answering questions. When searching for answers, both version of miss-tagging are a problem.
Now, let's look at the, so far ignored, final part of your question: are they really worth all the time and effort of maintaining them?
Yes, IMHO, anyway. To begin with, there shouldn't be that much time and effort to maintain them. The false positives are the easiest to spot, for an expert in them, and to correct, if not allowed to collect. The missing tags are a little harder to spot, though just as easy to correct once discovered.
When reviewing the list of questions, from a feed, a filtered view, or even in a full listing of the questions, a false positive is a cry for help. Even low-rep users can suggest edits to questions, and 2K+ rep users can make instant edits. Editing a question to remove a bad tag takes mere seconds, and adding proper tags while you're there is but a few extra keystrokes as well. When you see a tag false positive in one of your areas of expertise, take the time to help the community and fix it, before you forget. If, after doing a few of those edits, you get the sense that others may not understand how that tag should be used, then you are in a position to make corrections or additions to the tag wiki that might improve that understanding. Letting it sit in the back of your mind for a while before making any changes can probably result in actual time spent on the edit to a few minutes at most.
While the site is small, at <40K questions so far, it's easy to correct collected tag problems. If begun now there should be little need for massive efforts later, as has happened recently on the SuperUser stack in their Cleanup Weekend[¥]. One tag,
recovery had over a thousand questions that needed to be corrected.
There is an implied question in you question: is it worth my time and effort, to me, to maintain the tag system? For that I'd have to day it depends. It's good for the community, so how important is the community to you? If the community is important to you, then it can be worth your time, even if you don't get any direct benefit from the tags. And, someday, they just might help you after all. If you need an answer fast, you're more likely to find it using tags than not. Using experiments today, a search for
apache ssl[ŧ] returned 199 results, while a search for
[apache] ssl[ŧ] returned 113 results. The 43% reduction has already reduced your reading time in search of an answer. To make it even better, a search for
[apache][ssl][ŧ] returns 54 results, a mere 27% of the original with a consummate reduction in reading time to scan questions looking for your answer.
So, if you never need to look for an answer, don't use any of the other potentials of the tags, and are just here to display your knowledge without any connection or concern for the rest of the users, then maybe tags are not worth your time and effort to maintain. If any of those is not true, then maybe a small amount of your time and effort is justified. Finally, if all of those are false, you might need to find answers, you do want to access the power of tags, and you do care about the community and other users, then yes, it is worth the time and effort, including your time and effort, to maintain the tag system. Since you've already contributed to their maintenance with tag wiki edits, I think we know your answer anyway.
[¥] To be fair, the need for 'Cleanup Weekend' was triggered more by the cleanup of non-HTTPS images than tag corrections, which received more effort. Still, tag cleanup was a big part of their work, and still is, for that "weekend" which ran over the scheduled time by quite a bit. As of this writing it is still in progress.
[ŧ] Yes, I know that
SSL is not the preferred term,
TLS is. That was chosen to show the power of the tags. The final search automatically changed
[tls] before doing the search, which filtered out an additional 22 questions; questions you probably don't want to read when you need an answer anyway.