There is a weird situation that can occur when you are on very low health, where you no longer lose HP when typing correct letters, allowing you to finish the level as long as you don't make a mistake.
The HP regen upgrade is necessary, and perhaps the on-hit heal too. I'm not 100% sure what the conditions are, since it didn't happen on every run from certain point, but I believe you need to end up at some specific very low hp value.