With an up to date AGPS database, GPS is quite usable. AGPS is also distributed as a service, though, often by companies that made the GPS receiver chips. If that were to fall away, you'd struggle to make GPS usable for phones.
You may not need Google for a GPS lock, but you certainly can't get a good fix without an external party. I've unwittingly tried this, when I saw a weird HTTP URL on my network being polled in the background; I blocked it in my Pihole and found out not much later that my phone's GPS started taking longer and longer to get a fix. Not "waving your phone 30 minutes at a clear sky" long, but definitely to the point where using Google Maps with cell/WiFi scanning disabled become very annoying.
I run a modest fleet of mostly-offline data collection devices that rely on GPS; we pay a lot of attention to how long it takes before they can sync. With a good sky view, the GPS chip often has a 3D position lock before Linux has finished booting.
It's not really a limitation of GPS, it's about using the external service to let you minimize the time your GPS receiver is active. You can get a great fix without AGPS, but you can't both keep the GPS off 99.9% of the time _and_ get a fast, great position fix.
Yes, after waiting minutes with good line of sight for almanac and ephemerides to download from the satellites. Anything that gets a fix faster is already "assisted", usually either by fresh data downloaded online or not-yet-fully-out-of-date data stored locally.
I've been working on a phone that didn't have well-integrated AGNSS and used MLS for WiFi and cellular-based location when it didn't have GNSS fix. I'm perfectly aware that what you're saying is technically true, but try to explain that to the users :P
From the user perspective, it's not going to be a good experience if you rely on cold GNSS only on a mobile device (unless the user is already well aware of what to expect and how to behave).
Fair enough, I suppose. I think in the context of smartphones, continuously operating the GPS chip is simply not an option, but in other types of devices that isn't as big of a problem.
Fun fact: almanac and ephemeris data that makes (at least basic) AGNSS work is mostly available publicly, either from agencies that operate the constellations or from observatories worldwide. After reverse engineering the expected format I was able to feed the module I worked with with fresh data without having to use the proprietary (and unreliable) AGNSS service it came with.
You may not need Google for a GPS lock, but you certainly can't get a good fix without an external party. I've unwittingly tried this, when I saw a weird HTTP URL on my network being polled in the background; I blocked it in my Pihole and found out not much later that my phone's GPS started taking longer and longer to get a fix. Not "waving your phone 30 minutes at a clear sky" long, but definitely to the point where using Google Maps with cell/WiFi scanning disabled become very annoying.