Google therefore has a difficulty
If Google had found itself in this position by accident, I might have some sympathy. It set itself up as the distribution service for Android apps, made itself the arbiter of worthiness and takes a cut from the sales - it just needs to do it better. Google's usual approach seems to be to half-heartedly get something more or less working and then try to forget about it: perhaps it's time for a change of tactic?
I don't personally find the Play Store to offer much in the way of curation. I'm undecided about whether it offers much in the way of security - a better permissions model might be more useful, and then they wouldn't have to run the store at all.