Earlier quoted context omitted.
Some would take enhanced privacy over properly-functioning sites. I wonder how broken sites would appear if the browser simply lied about such things.
There’s like a billion side channels to determine how big the screen is unless you just want to entirely break basic css. Which is a pretty unreasonable way to address this problem.
Edit: Having a bunch of html buttons/links, showing a different to agents based on their resolution and waiting to see which ones they follow would break this, unless everyone crawls a lot of stuff they don't need. Pretending to be one of a few common sizes is probably a better solution.