forces - Adhesion vs Static Friction

I feel like this question should have a simple answer, but I haven't been able to find one anywhere. I hope someone can help:

In short, my question is why the force of static friction is so much greater than the adhesion force between two surfaces. If they're both caused by the bonding of molecules on one surface with molecules on the other, why is it that it's so much harder to start sliding one surface across another than to just pull the two surfaces apart? (Look at edit!)

That's the question, for more details I want to explain how it came about:

I was looking at the case of "rolling without slipping". Let's say a wheel is rolling at a constant velocity: the reason there is no kinetic friction is because the point of the wheel that touches the ground gets lifted off straight upwards, and never actually slides relative to the ground.

But then say we exert a force on this wheel, making it move faster, but still roll without slipping. If it's moving faster, the wheel must now also roll faster in order for the point that touches the ground to not slide. There must have been a force (torque) applied on the circumference of the wheel to give it some angular acceleration.

We are told by most sources that the force came from static friction with the ground, and it was caused by static friction with the ground, which for rubber on asphalt, is apparently relatively high.

Now, I'm no expert, and I may very well be incorrect, but I've learned that this friction is in turn caused by (London dispersion?) bonds forming between the point of contact of the rubber wheel with the road.

But, if these bonds are strong enough that they prevent the wheel from sliding, why don't they also prevent it from "unsticking"?

Thank you!

Edit:

My assumption of the cause of friction is the root of the problem. I explain it more in an answer.