Wouldn't be enough to see more ZEC exiting from the private transactions than those entering, to know that ZEC is compromised?

I have seen some people claiming that it would be impossible to know if Zcash is compromised, but if we have more ZEC leaving private transactions than entering, it would be sufficient confirmation, wouldn't be?

If we had more ZEC leaving private addresses and going into public addresses, I agree. But what about if we have ZEC going from private to private addresses?

In that case I think it would be almost impossible, but I think that would depend on how common private transactions are, since private transactions are kind of inconvenient by the extra waiting when signing private transactions.

Paradoxically, the most private Zcash is, the most difficult it would be to detect someone exploiting some bug to print ZEC for free

I think someone being able to hack the system and effectively print ZEC would be equivalent of the government printing fiat currencies. Even though you don't see each individual transaction with fiat currencies, you still know that money is being printed because the cost of goods goes up (and other effects of inflation).

It would be far worse because the whole network would be at the mercy of an unknown entity whose intentions would be also unknown. It could print 1 billion ZEC in one day just for the lulz