It depends on the specific model, but Ubuntu Touch will run on some Pixel phones and at least used to support running Android apps using Anbox or Waydroid.
The biggest problem with it is that VoLTE is not supported yet on Qualcomm chipset phones (of which the Pixel is one). The developers are definitely working on that, but they a very small team of volunteers so they can only move so fast. For now that means Ubuntu touch phones in some markets, such as the USA and India, cannot make or receive calls on the mobile network.
Mobile data works though so there are workarounds using VoIP or services such as Telegram or Signal if you're wanting voice capability.
Would you mind sharing how recently and on what phone model? I had it on a Nexus 5 using version 18.04 and the battery life was indeed awful. I upgraded to a Pixel 3a and then the developers re-based the OS to 20.04, and now it seems to be lasting much, much longer on a charge. I admit I don't use it daily though, since I'm in one of the markets that needs VoLTE. This is just my perception.