Contact pressure? Why would you care about something that has less of an impact on traction than surface area? The size of the contact patch will have more of an effect on how much grip you have than how much pressure is on it, that's why we air down.
What's best depends on conditions and terrain. For my needs narrower is better.
Also, one reason people air down (whether they know it or not) is to get the outer lugs to contact the ground more. Narrow tires already do that more at normal street pressure (have flatter contact patch at street pressure), which is part of why I don't need to air them down for Winter roads or moderate off roading. I only need to air down for extreme stuff.
Narrower certainly is better for gas mileage too.
And before someone goes "well winter tires are narrower so ha!" Winter tires are narrow to cut through the snow and get to the road beneath instead of floating on top of the white stuff.
You just perfectly described how more contact pressure from a narrow tire helps in Winter. In the same way it reduces or prevents hydroplaning at high speeds on wet highways (very wet with puddles like we have here).
Also, narrow tires are lighter (if comparing same brand, model, rim size, and load rating).
I like that narrow tires don't stick out as much and offer more clearance to sway bar and LCAs during turns.
In my prior post I didn't say narrow is better. I said I prefer them (for my needs).
In this post I didn't say narrower is better. I said narrow is better at some things,
which are the things I care about most. Wider is better for some things. For some things it makes no difference which.
For example, a 31 x 10.5 R15 (or any 10.5) would improve my sand and beach abilities due to less contact pressure (more surface area) helping me float on top of sand, but a 31 x 9.5 R16C (245/75R16C) would improve my Winter road abilities due to more contact pressure (less surface area) helping me sink down and cut through snow to grab pavement.
Winter traction is more important to me than playing in the sand. That's just one example of why I prefer narrow. I could give many other legitimate reasons, but don't want to type more.
There are legitimate reasons why some guys prefer wider tires for their conditions and priorities. I'm not attacking their choice.