People in leading positions who leave for competitors get told to not show up again, but of course get paid so it is a paid holiday.

To be fair, these rights extend in both directions. This may seem extreme from an employer -> employee direction, but I have the right to do the same in reverse: I could call my manager at 8:30AM tomorrow morning and quit on the spot with no justification.

At Will employment cuts both ways.

Except the power dynamic and consequences are (usually) totally different:

Company fires their employee at 8:30AM on the spot: Employee is now without income and likely health insurance and his ability to pay rent, buy food and merely exist might now be in jeopardy.

Employee quits at 8:30AM on the spot: Company is at worst set back a bit until they backfill that job. At best they don't even notice. Unless that employee was some keystone that held the whole business together, there is no existential threat to the company.

In addition to that, it's considered "unprofessional" to leave without giving at least 2 weeks notice.

I don't think I'm being arrogant to think that my employer would have a harder time replacing me than I would them.

If that's actually the case then you're in an extremely fortunate position, and probably something like the top 2% of the income distribution.

It is not fair. Fair is when you write resignation letter or receive a termination letter and continue to work for the next 3-6 months. That is fair!

Ps: without at will system you can simply stop showing off at work with the same results.