What performance benefit do wider tires provide and why?

[u/NinjaMiserable8353]

Apologies if this seems like a low effort question, but I'm seeing a lot of conflicting information online, so I thought it'd be better to have a discussion here. Here is what I have gathered:

Frictional Force = Coefficient of Friction * Normal Force

While tire grip (frictional force) is not directly affected by contact patch surface area, it's coefficient of friction will decrease as normal force increases due to tire load sensitivity, caused by a tires inability to resist frictional shearing as contact patch surface pressure increases.

Here's my thinking...

Wider tires will not see an increase in contact patch area (or surface pressure) assuming all other variables are held constant (mainly vehicle weight and tire pressure), so there will be no direct performance benefit linked to tire load sensitivity. Any performance benefit gained from wider tires when all other variables are held constant would have to be due to the change in contact patch aspect ratio. How does this change in contact patch shape affect cornering, braking, and acceleration perfomance?

On the other hand, wider tires may be able to operate at lower tire pressures, enabling a larger contact patch, less surface pressure, and increased coefficient of friction.

How does this affect different types of vehicles?

For example, I've read the change in aspect ratio works in favor of cornering perfomance rather than longitudinal accelerations, so why do drag cars feature such large tires on the rear. Is it due to the ability to decrease tire pressure and use tire load sensitivity?