Logs are important resources for troubleshooting, even for deployed software.
I would limit the registration of product releases (perhaps I even limited it to "enter emergency situations"). But I would not categorically say "without registration".
Here is a good discussion (with some good recommendations):
PS: Having said that, I hasten to add:
No, you should not have any "debug" or "informational" release logging.
This is exactly what the Android documentation says in the links above.
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