Does this then imply I don't have a right to live, because "rights cannot be denied based on the ability to pay"? That I don't have a right to property, because if I don't pay my debts my belongings can be confiscated and sold at auction?
I have a right to appoint my own counsel, but the government won't pay for the counsel I appoint. In order to use that right I have to be able to afford the lawyer I want.
US citizens have a right to run for elected office, but clearly that's not provided free of charge!
Rights are not irrespective or independent of my ability to pay. And if something is a right does not mean I get it for free.
I think you need to lay out your argument in greater detail than you have done so far.
To say that carriers should be able to selectively revoke this abstraction and deny travel to specific individuals is to give them the power to force arbitrary rules on anyone who relies on this infrastructure. This would make all rights subject to the whims of the airlines.