What if you needed to recharge your PSP battery while playing? It had video out, but it was never designed for a couch experience. It was the typical Sony let's do all the things at once mentality. No one bought it for that reason alone, but it, and all the other weird features of the PSP, probably helped it become the only viable portable competitor to Nintendo in 30 years.
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.
Too bad Sony then decided to get rid of the video output in the PS Vita even though it was possible (the dev kit had HDMI) and contrary to the PSP it actually made sense as at this point mobile hardware was so much better due to the smartphone industry. One of many small mistakes that made the Vita much less enjoyable overall.
The (affordable) technology of the time didn't allow for easy dock/undock experience like the Switch does. That doesn't mean it was "just a marketing difference," the product experience was worse and wasn't designed to easily be used as both a portable console and a dedicated living room device.