Cyclists travel slower than the prevailing speed of motorists, and they accelerate from a stop much slower. And while they don’t take up much space, the space they consume is not zero. We can argue the magnitude here, but the effect is obvious to anyone who has shared the road with a cyclist.
Road wear is not the main issue. Roads will deteriorate whether they’re used or not. They will deteriorate faster with heavier traffic, sure. But deterioration from temperature cycling, road salt application, and weather happens whether they’re used or not. If cyclists want to use this infrastructure, they should contribute to its upkeep.
If cyclists have a car and contribute by paying these taxes and fees, then let’s build a regulatory regime that exempts these users from cyclist fees and taxes. The point here is to make those using the infrastructure pay for their share of upkeep and their contribution to congestion.
Deer are only a danger to themselves too, right? People never experience damage to their vehicle or personal injury when they hit a deer? The damage and risk is not proportional to both parties, sure. But it is false to say that drivers experience no risk of damage or bodily injury when in an accident with a cyclist who disobeys traffic laws. Cyclists should be insured at whatever rate is necessary to protect against this risk.
Your school children example is not really applicable here. We’re discussing cyclists who want to be treated like motorists but refuse to act like them and obey common traffic rules. That is about as far as you can get from from an innocent group of school children crossing the street with the flashing red stop sign on the school bus activated.