Wouldn't a smaller screen with a thicker phone last longer? Less screen area to light up.

I'm curious what the tradeoff is on increased energy consumption is with the larger screen / larger battery / thin phone setup.

Yep. A screen's power consumption grows with the surface area of the screen (w * h) whereas a battery's capacity grows with the volume of the battery (w * h * d).

I think the dominant market pressures so far has been practical concerns like phone thickness and battery life so manufacturers - who are all also competing with their past products - are forced to sacrifice screen size options to compete. Now screen size is becoming unwieldy and screens/batteries have steadily improved so we might swing back the other way.

You could double up on gains on a smaller phone by reducing the screen resolution, which reduces the power demand on the chip managing the display, and so on. Back when I had the Nexus 4, at 720p, I never felt it was pixelated or annoying. Then again, I don't watch movies on my phone either.

On the other hand, given an OLED screen, where energy cost only grows proportionally to the number of pixels receiving power, you could slap a big screen on the phone "for watching movies" but have the phone display a smaller screen centered on it (with black bars around) most of the time. I have a feeling this is the direction the industry would go, if battery life truly became a concern.

I would be happy if they added 1mm thickness to my SE and left the rest. That would allow for quite a bit more battery.

The impractical aspect to that idea is that it would mean creating a new accessories variant. Keeping the same physical dimensions as a previous phone means compatible cases are already available from hundreds of accessory makers.