Honestly, I think you are just using a very specific (and pretty inaccurate) definition of a personal computer. Also, a strangely specific usage of “arbitrary”. All of the cases I mentioned (chromebooks, immutable distros, enterprise windows with administrative restrictions) intentionally lock out the user from running software the hardware could otherwise support.
Saying a device that the manufacturer artificially locks out users from installing non approved software is somehow related to the definition of a PC is simply a lie.
You can install Linux on smart phones, so by your definition, a phone is a PC. You can install Linux on first gen switches without modifying the hardware, so by your definition, first generation switches are PC’s. You can even install Linux on modern switches just by soldering on a special chip, so “modified switches” are PCs.
ATM’s often run Windows as the base OS ffs, of course you could call them a PC. As you said;
the owner of the hardware “running arbitrary software” to control what someone else can do is completely irrelevant.
If account restrictions are the “owner of the hardware” preventing the end user from “running arbitrary software”, then all that means is Nintendo owns your switch. Not that the switch is incapable of running arbitrary software.
Your strange definition of PC simply does not hold up to scrutiny. I get that you are trying to say that “because a Switch is a device manufactured for the express purpose of running games only accessible through Nintendo’s official channels, it is a far different user experience than what we think of as a traditional desktop”. But to say it isn’t a personal computer, when it is a personal device that runs software using a processor, ram, storage, a graphical processor, all connected by a central print circuit board is simply absurd.