It's not a bug.
I don't know how the system determines what suggestions to show there, but it is completely different for me (logged in/out, different devices). It almost seems to be random.
[...] it's been deprecated for a long time [...]
Let's not forget, the homework tag is deprecated as a result of our meta discussions. The system itself doesn't know anything about that. And while we have been actively cleaning out the huge pile (≈ 2,800 uses as of Do we really need [homework]? [Part 3] to ≈ 1,100 uses as of now), it still remains one of out top 10 tags. There simply is nothing special about the tag.
That being said,
it's not a problem.
In the spring cleaning chat we keep track of every question that gets newly tagged with it. I think it averages out at 2-3 times a week since we pulled the questions in with a feed (That's a feeling, not hard facts though.) I wouldn't actually consider this a problem.
So, what now?
Since the somewhat clunky handling of the [reaction] tag, (I think) we decided to handle this case differently (If you are interested: Should we delete and blacklist [reaction]?). We thought the best approach (this time) would be to first discourage the usage (that pretty much worked), then silently clean out the existing cases (so much work), if necessary blacklist it (I don't think it is strictly necessary, do it if it reappears; new users cannot 'invent' tags, so they are not the problem).
Nothing much; keep calm and carry on. We cleaned out ≈ 1,700 cases in the last 20 months or so, interpolated roughly, we'll be done with this in march next year. Although I have to mention, we cleaned out the worst cases first, where the decision was most often to simply delete the question. Now there is more to loose, so more to work through and we'll be slower. So let's adjust this conservatively... we'll probably be rid of [homework] by Winterbash 2020.
Of course, anyone willing to help out cleaning up is more than welcome to do so. (It is currently about three people, not all of them having a lot of time recently.) The more people review the questions, the sooner we will be done just a few more cleanups and it'll drop out of the top 10. And the fewer cases there are, the fewer times it will be shown to new users.
In the spring cleaning chat we're not simply deleting questions, or detagging them, we'll also reformat, streamline, occasionally reopen them. You could be part of that! :D
Addendum re: feature-request
I am strictly against taking any action; I just want to make this abundantly clear. Apart from blacklisting the tag, I do not think there is anything we could do; I explained why I don't think we need to do that above.