If that were the case, surely Tour de France riders would use wider tyres to gain more grip going around corners, especially in time-trials or stages with sprint finishes. Doesn’t a greater surface area touching the floor means more frictional effects when pushing against the road?
Good question because at first I thought it might be negligible due to the tire normally being in a state of static friction relative to the road. But some quick searches showed me that rolling resistance is related to how large the contact point is, like you suggest, along with a variety of other factors. https://en.wikipedia.org/wiki/Rolling_resistance
I don’t know how reliable this is, but googling brought me to this site which compares bicycle tire brands according to rolling resistance on their test machine. Apparently, some 25s have all the 23s beat. If true, the variability range for bicycle tires is a lot wider than I expected. https://www.bicyclerollingresistance.com/