Since Google rules the OHA (Open Handset Alliance) with an iron fist, there's no way on earth an OEM can brand its devices "Android" without Google's blessing (read: installing Google Apps in the /system partition which no user can get rid without unlocking the bootloader). And more and more of the open source parts of AOSP have been left to rot, in favour of "Pixel-only" apps. How many years has it been since JBQ quit AOSP in protest? And what has changed?
> If you want to get quick updates from Google, vote with your wallet and buy an Android One phone.
Those who voted with their wallets, got into a program which Google all but abandoned. Some OEMs like Nokia (HMD Global), Motorola (Lenovo), and Asus continue to ship seemingly unbloated Androids (but not as part of Android One). But credit where due: GKI (Android Common Kernels), Treble, APEX, pKVM (microdroid), TEE OS will pay dividends in the coming decade, essentially superseding programs like Android One.
Google's Android is not Samsung's Android, nor is it OnePlus' Android. They are all forks of the "original" AOSP Android and should be treated as such. Google requires some compatibility for inclusion of their Play services and has used AOSP to build in the core to achieve this, but it includes only very specific parts of the operating system.
Google Play is an application package that's added to another operating system, and an optional one at that. Huawei is still selling phones without GPlay and people are still buying those, even outside China.
There are phones for which your arrangement actually works: the Android One programme has Google set up everything but the drivers and associated libraries for vendors, who can then push updates to end users almost directly from Google.
If you want to get quick updates from Google, vote with your wallet and buy an Android One phone. Most manufacturers prefer to have control over their own stack so they can add distinguishing features to their products, plus there are obviously fees for the OS involved, so the price may be higher for some Android One phones compared to the other products, but you do usually get the updates in the way you describe.
At the end of the day, though, the average end user doesn't care about Android One. The option is still out there if you care.