And yet if you want applications to work on your phone, many times you'll need approval from either Apple or Google. Google can effectively ban manufacturers (like they did with Huawei) from using "Android" by blacklisting them from Play Services. Apple owns the entire ecosystem and prevents third-party from having access to the same feature set.
Look up Play Integrity, it's the remote attestation framework Google uses to ensure apps only run on Google-blessed hardware and software. Apps that use it verify that both hardware and software are unmodified and blessed by Google before apps are allowed to run. Banking apps use it, the fucking McDonald's app uses it, public transit pass apps use it, etc.
If you want to use your phone like normal people do in 2025, and not relegate yourself to being a second-class citizen when it comes to simple things like paying for stuff, riding the subway, etc, your phone is either an iPhone or something that plays nicely with Play Services.
And that's just the remote attestation side. Many apps rely on Play Services themselves, and without access to them, will not work. Google gates access to Play Services through contracts, it is not open source or part of Android.
You need to allow Play the play store and it's services and those will wall you in. Many times discussed here: many banking, gov, health apps around the world are banning anything not blessed by Google or Apple and installing on a non blessed system will not allow you to use them. My bank allows a modern and supported android or ios phone or a Windows laptop with a biometric card reader. Pretty much locked in and all banks are following.
Something tells me that the thing about Google not allowing custom Andriod operating systems to install apps is not quite true. I don't know about this specific topic yet, but I bet that if I look into it, I'll find out that there's nuance here that isn't been correctly portrayed by your comment.