It looks like you're new here. If you want to get involved, click one of these buttons!
Do wider tyres provide more grip because there is more rubber on the road? When you use a wider tyre you alter the contact patch to be wider, but it reduces in length. So depending on sidewall stiffness, a wider tyre can actually give less rubber on the road (assuming the load/pressure/compound remain the same). The main reason for tyres being the size they are is actually heat management. Wider, low sidewall tyres will cool better than narrow tall tyres. If you can't get a tyre up to temperature it will provide low grip.
Eg. Rally cars use wider tyres when on tarmac rallies, and use (surprisingly) very narrow tyres on ice rallies.