If they are desperate enough to chance it to fly late into pregnancy to here for the free service though, what is the chance of them being able to pay any fine levied or to enforce it, especially if they return to where they came from or otherwise disappear.
The problem is, so long as the door is open people will walk through it, they can so will. To an extent, can you really blame people who walk through an open door? It is the cause that needs treating rather than blaming the effect. What hospital can turn away a mother giving birth.
If medical evidence can be faked, pregnancies concealed etc... realistically, how could the airlines prevent pregnant ladies flying late save going into the realms of their own medical examinations. It's not like fining drivers who have illegal immigrants hiding in their vehicles, save checking themselves, which would be a minefield in itself.