A Tumblr-style tag field is another possibility, sure. (The hash just is the symbol of tags these days, just like links are blue, so 'hashtag' just means 'tag'.) Tags would be per-post, not per-thread, so it wouldn't be possible to fit them into the thread title anyway — maybe you could get an index of the tags used in each thread, but it couldn't be listed on the forum page, since there wouldn't be enough room.

Inline hashtags have one advantage — it'd be slightly easier to add them in long text posts. If I'm writing a post like the first post in the non-European phonologies thread on the ZBB, I can write, say,

The #uvular_nasal almost never occurs contrastively*, voiced uvular fricatives are uncommon, and holes in #uvular stop series are frequent: #Georgian only has /qʼ/, #Avar has only two short uvular consonants, #Uyghur has /ʁ/, and #Chechen, one of the few languages with both uvulars and a large vowel inventory, is missing /ɢ/. According to #WALS, it's slightly more common for a language to have uvular stops and continuants than only uvular stops, and a bit over three times more common for a language to have only uvular stops than only uvular continuants.

...instead of having to remember to add the #uvular_nasal, #uvular, etc. tags at the end.

But on the other hand, that'd be ugly — doubly so for tags not used in the post text.

I'm not sure which option I prefer. If I'm writing a long post, I can just add the tags as I write.

(I briefly imagined an option to type a hashtag in the post field and have it automatically transfer down to the tag field — so if I type "...holes in #uvular stop series...", it automatically erases the hashtag from #uvular and throws a #uvular tag into the tag field at the bottom — but that'd be way too much Javascript magic and it'd probably lag my shitty-ass browser to hell. There's a tradeoff between the minor inefficiency of having to enter tags and the major inefficiency of having to load down the post box with JS and Firefox crashing every five seconds.)