Do failed (bulleted) misisons count?

Do failed (bulleted) misisons count towards your max?

If they do, that makes the broken Fxxx behavior even worse as bulleted mission will continue to pile up, and having no way to get rid of them without using abort.

If they don't, then is that a way to get around the max?
(for the purpose of using the abort function to create changes - seeing as a mission that's failed can still be triggered using the abort function.)

What is the goal of the mission? A failed mission should be removed once you return to returnstel. Could you make it so that once you fail it disappears at the next stellar you visit?