Derpibooru lets you watch tags and artists, so why can't e621? I think it will be very useful. What do you think?

It would be nice to have. Personally, I have Wolf's Stash on my phone and Hydrus Network on PC that basically have this functionality already, so I probably wouldn't use an integrated system if one were released.

if you got tampermonkey then there's a quasi-official userscript called re621 which has a shitton of qol features including the ability to watch tags (i say "quasi" since it's made by a former admin)
https://e621.net/forum_topics/25872

+1 for re621. I use it to watch tags and it's very good at it, especially if you're a fan of tags that aren't super popular and can slip under your radar if not searched for frequently.

I just wish I could figure out why Tampermonkey doesn't play well with my Firefox browser; TM causes it to load for several minutes when initially opening the browser, and often doesn't load at all until I open the TM menu on my extensions bar, and reloading the webpage. *shrug*