This reply by @manton is from 2018, so there might be another reason now. 
Micro.blog on the web uses a custom text box for Markdown highlighting which prevents spell-check from working. Still evaluating options to replace or disable it.
It should be solvable, though.
On the topic of spellchecking, if you’re concerned about privacy and security, here’s an article worth reading: Chrome & Edge Enhanced Spellcheck Features Expose [Personally Identifiable Information], Even Your Passwords.