As a user, I don't care at all if it makes dev's life easier. I bought the app and don't want my personal info to be leaked.
It might be one more place to screw up, but so is just having more actions your app can do.
I'm not sure I see any difference between an app recording all I traction within it (for single purpose apps, but not browsers) and a store video recording everything in it.
Correct. The payment code is usually gone over with a comb for PCI compliance (or completely outsourced to someone like Stripe), whereas the UX tracking is much less so. It's also a common enough issue that stuff like credit cards or API codes end up leaking into logs.
That said, my point isn't necessarily that you should trust apps gathering UX metrics more, but that you should probably trust all apps quite a bit less, whether they track user actions or not.