a thing that sucks is theres also no good way to view alt text as a sighted person (twitter no longer makes it visible when you click the alt button) outside asking alttextbot, so a lot of people just don't learn from example...
I use ctrl-shift-c for inspect element when I really want to see it. I haven't bothered finding a trustworthy/robust extension since I'm fine with that approach.
I do use the Twitter Required Alt Text extension to remember to add alt text before posting a tweet or it's hopeless.
The user interface encourages you to add the image and post. I'd usually remember right after I tweeted it. The extension fixes that problem.
I'd never forget when writing HTML but Twitter's user interface isn't set up to ask you to add it as a standard thing when it should.