Please don't mix finger print sensor and touch screen. Not the same, sensor is based on metal ring around.
As I've said, the METAL RING is based off capacitive technology JUST LIKE A TOUCHSCREEN. It needs to be touched by a skin of a living being for it to trigger the SENSOR which is the white/black circle glass in between. Two different parts, combined for a purpose.
The extra button press is to activate the ring which in turn will activate the sensor.
Goes like this:
Press Center, turn on screen -> Activate Ring -> (Ring verifies living skin cells) -> Activate Sensor -> unlock phone
What you're proposing:
Rest finger on ring + sensor -> (Ring verifies living skin cells) -> activate sensor and screen -> unlock phone.
Problem: The ring technology (not the sensor) only senses living skin (not finger cells not finger electricity) so when you rest your nose on the ring, it will activate sensor and screen, then the sensor will have failed authentication because your nose is not registered.
This will be a bad scenario for: phone in pocket, phone TouchID ring grazed etc.