Even with 80w-120w chargers these days?
To rephrase your question:
Could we build a new phone that runs off a 80..120 W charger without battery? Absolutely yes.
Will it help older phones that were not designed to use such a charger? No, most likely that charger will change nothing.
Now you have to have an extra decision circuit that judges whether or not the wall is "good enough to boot the phone" and then ask if it's good enough to run it as well. Last thing you want is wall power to dip randomly and you can't switch fast enough and simply shutting off.
I understand why you would pick the battery as the requirement. You know the exact behavior of when the phone is safely bootable vs not w/ a predictable DC signal.
You can throttle the CPU. In fact you should, especially if you expose it to the public, to prevent it from overheating.
Apparently some manufacturers put the phone's NFC coil inside the battery instead of on the phone's back housing, so there could be a fourth pin for that. Or perhaps the battery contains its own microprocessor that answers a DRM challenge from the phone specifically for the purpose of blocking out third party battery manufacturers. Etc. etc.
Still there is the problem that the phone might have peak power usage above what its charger can provide, so you'd have to use a wall adapter with a higher amperage rating.
Ah yes, good old anticompetitive practices. Sleep well, FTC.