I agree that the blanket term “computer” is fading in favor of more specific terms- desktop, tablet, smartphone, laptop, PC, etc…
An analogy might be that “computer” is akin to “vehicle”, and most people refer to cars, bikes, motorcycles, boats, airplanes, etc… by specific name most of the time.
I don’t call things a computer unless I’m getting really specific. Even my desktop I usually call a PC, which stems from “PC gaming” which I do most often on it.
(Yes, I’m aware PC has computer in the acronym)
My wife and I both say things like “I’m going to play on the computer” not laptop, but then our laptops are connected to wireless keyboards and monitors, and so aren’t used as pure laptops.
Nonetheless I agree with the OP. I think the reason is that computing devices don’t look much like whatever model of computing device you have. When I was a kid it was a mainframe in a glass room. But even if you grew up with a computer looking like a desktop you can be forgiven for not thinking your phone looks much like a computer.