The first thousand USD/mo a person earns has a different meaning to them than the second thousand, and the third thousand, and so on with diminishing returns. The point of minimum wage should be that no one is constantly fighting for their life, because a person in that situation is usually a harm to everyone.

we could just gradually keep hiking it until it starts impacting employment and then stop.

stage 1 is it hammers profit margins <-- for 95% of businesses we are here.

Stage 2 is then it increases prices <-- only affects very low margin businesses which are a small minority.

Stage 3 is it triggers job losses <-- to my knowledge it's never been raised high enough to make this happen. maybe $50 / hour would be the threshold.