Could white have done better?
Appears that black has lived in gote as a and b are miai.
Alex: Yeah. Pushing in like this is one of the bad habits I talk about in the book I'm working on. Most kyu players play something like this several times a game. Some times, it's more harmful than others, but I think simply ceasing to push in when you can't/aren't going to cut is enough to gain a stone strength, because those who commit the mistake commit it so often.
unkx80: I will also consider . Because of the stones, there is no escape for Black.