If a device has proper battery management, then it should be able to run all the time on USB, with the battery serving to supply power when the USB power is offline.
Poor battery management could result in batteries not surviving... potentially dangerous if the battery starts swelling up.
As for running older phones and tablets that have had the batteries removed (due being worn out or swollen) most/all? will not run on USB alone, as they need to "see" a good voltage on the battery connection. This is done by wiring 5v to the internal battery connectors, in place of the battery. The phone should have internal regulation, so the 5v will not hurt it (worked for me for over a year).... just NO higher, even if the device supports "fast charging" as that is only through the USB.
Best done with a device that has a user removable battery, but some careful effort removing the battery and very fine soldering work will convert any phone/tablet to full time wired.
