Sure, it is technically a trivial one along with other functions. But it doesn't feel sensible to call it a router because that's not its defining charcteristic. And the business of nontrivial routing that goes on in the devices whose full-time job is to be routers is different, involving routing protocols and stuff.
I understand it's a little bit dumb that many people think of a router as a device that does Wi-Fi and maybe has a modem built-in, just because that's the only kind of router most people ever encounter. But for all that it's annoying and technically not quite precise, that is the colloquial use of the term.
> The term "CPE" seems to be more about device ownership than technical function.
Not ownership, location. CPE can be owned by the network provider or by the customer.
But it indeed doesn't have a clearly defined technical function. CPE can be just a modem, a consumer all-in-one device, or a "proper" enterprise-y router from Cisco/Juniper/...
