By forcing airlines to allow horses, that means the airlines have to expend effort for that. That means they have to raise prices. That means all airline fliers are paying for it. I don't see a reason why all US citizens should pay for it instead of all US fliers paying for it.

As far as depriving other passengers, it's up to the airlines how to do that. They are incentivized to provide a good experience to fliers in order to keep people willing to fly with them.