You plug it in? It's literally plugged into your TV already it's not a big deal to plug the AC adapter in the other side. The PSP Go had a dock for connecting to your TV and supported using a DS3 controller for TV play. Of course nobody bought a Go and nobody bought a dock for it. But they did kinda sorta get the concept.
How would I plug in a Switch in that case? The Switch actually requires AC to use the bundled dock whereas you can use a PSP hooked up to the TV on battery power. The PSP video cables are not THAT long. If you can plug it into your TV and use it you can probably plug in the AC adapter. It's a weird complaint when the Switch also needs power and uses a more annoying wall wart design than the brick in the middle that a PSP uses. And again the PSP Go supports a dock and wireless controllers. The concept was clearly there just half-baked.
The reason the PSP was not considered couch adjacent is that the first model didn't have the feature entirely, it was never bundled in the box and had limitations with regards to PSP games (they play in a window) and no seperate controller support until the Go. Since it was always optional it was easy to ignore.
I didn't mention anything about the Vita either...Sony pivoted too hard towards the mobile market with touch features that prevented TV play. Early versions of the OS didn't even allow navigating with buttons. It was one of many mis-steps of the device and caused problems for the PSTV down the line.
