There are several that come to mind.
Drag is due to rolling resistance at the contact patch, bearing resistance, and wind drag. These all operate with different scaling laws, both with respect to speed, and size.
Inertia is very important to the feel of a bike. Getting the caster and inertia right for the bike has a huge effect on steering. Wheel size affects weight, and therefore inertia.
Wheel size affects the gearing needed. This is the big one for conventional chain drive bikes. If you want reasonable speeds, you need a decent sized rear wheel because of the constraints on single stage chain drive gear ratios.
Propulsion and braking. These often aren't equally distributed, and you need to provide acceptable tire wear. You can do it with width or diameter. But in the case of a farm tractor, width is constrained by the space between rows.
As a kid, I owned the only bike in town with a 24" rear and 20" front tire (thanks dad), and I got made fun of over it. I was not aware of any offsetting benefit at the time. Although the practice I got from being chased probably helped me to become a competitive racer later on.