When it comes to running patched operating systems, Google's phones are pretty much the only ones that provide a decent option for running secure and user-controlled firmware. It's every other vendor, from Apple to Xiaomi, that's preventing people from doing so.
That said, there are a few companies out there that will happily put your brand and your firmware on their hardware. That's how the Trump Phone was made, the biggest example of this practice in the west. Other utility brands have been releasing cheap crap branded phones for years (like the Gigaset smartphone). You'll need money upfront and a decent minimum order quantity, but getting phones with firmware you control straight from the factory is still an option.
Obviously the Google Play features being available only to Google are a problem, and it's good that the EU is forcing Google to cut the crap, but Google's restrictions aren't the reason companies aren't running custom ROMs. It's pretty much everyone but Google that's at fault for that, from vendors restricting user freedom to app developers restricting their apps to Google Play certified devices only.