I don’t know.
Since USB is all 5 V, the chargers differ by their current ratings. If your device complains that a charger is inadequate, it means that the charger’s current rating is inadequate: Either it’s not advanced enough to be able to negotiate currents higher than 1 A, or it can negotiate but knows that it can’t safely deliver as much as the device would like.
Most likely, if you plugged a computer into a charger meant for a phone, it would complain about it and charge only extremely slowly. You might even need to turn it off for it to charge at all: It might otherwise be getting less power from the charger than it uses for standby. On the other hand, plugging the phone into the computer’s charger would be hunky-dory all around. In no event should anything be damaged, provided everything follows the standards.
Of course, that’s a non-negligible “if”. There are a fair number of devices that use USB-shaped plugs but which don’t follow the USB standard. Caveat emptor.
That may be true of USB 2.0 or 3.0, but the computer chargers I mentioned are USB-C, which can carry higher voltages and wattages.
But the part where you said “USB-C is a standard just for the plug and cable” wasn’t informative. PD (as used by a USB-C charger) is a standard protocol, negotiation and set of “Power Rules” which define a set of voltages and current, backward compatible with USB and BC 1.2 signalling.
I don’t think I’m the one who said “USB-C is a standard just for the plug and cable”.
A simple low-drop-out switching regulator will burn out if fed a low voltage. It will draw more current, which will pull the supply voltage down, so it will draw more current, which will pull the supply voltage down — until it exceeds it’s own current rating and burns out.