Drivers can see the walk signal too. It serves as an extra reminder to look for a pedestrian. If it's on every time, then it conveys no information about whether there's a pedestrian this time.
For example, I'm standing on the northwest corner, facing east and waiting to cross. A car is also facing east and will be making a left turn across my path. Ideally every driver looks all around, so they'll see me 90 degrees off to their left, but in practice drivers tend to look in the direction they're going to be driving. This means their field of vision includes the walk signal but not me.
For that matter, I wouldn't hate the idea of expanding the button's functionality to advertise my presence even more. Like sticking a flashing "PEDESTRIANS PRESENT" light right next to the red/yellow/green light.
A far better system for connected vehicles would be pedestrian signals that are always green for pedestrians by default, which will change to permit vehicles to pass when vehicles are present. This is very expensive though. Far better and cheaper to just ban cars.
This is what is described as a "beg button" by urbanists. Requiring pedestrians to press a button to give them a safe window in which to cross doesn't account for situations where pedestrians may not be able to request to cross due to construction, disability, or other factors.
https://usa.streetsblog.org/2017/03/24/seattle-campaign-to-g...