Matchlock and flintlock muskets had poor rates of fire compared to the bow, but soldiers in China, Japan, Europe, and even Native Americans adopted them. What were the reasons for this?

Ah yes, the matter of early firearms. It's not just about rate of fire, you see; it's a fair bit of other factors. If anyone would like to put their oar in, please go right ahead! In the meantime, OP, as the matter pops up every so often, I commend to your attention these previous posts:

u/wilymaker has an excellent two-part breakdown on this matter,
and there's a section of the FAQ devoted to this question. (In case your browser doesn't take you there directly, it's 'Weapons Development', the subsection named 'Transition from Bows to Firearms'.)