I know nothing about the airport covid test. However, I do know a great deal about Mexico. And what I know is that there's always a chance for chaos and incompetence.

You'll probably be able to get the test done at the airport with no difficulties. However, it's also possible that:

The staff doing the test at the airport goes on strike.

The testing station is inexplicably closed, with airport staff telling you "they'll be back in five minutes" for three hours.

Some critical piece of machinery breaks.

The health ministry didn't provide them with something they need, so no tests today.

The one person doing the testing tells you, "No, actually, the results don't come back for three days; the website is wrong."

You see where I'm going with this?

Pay the $50 to get it done ahead of time.