Let's not forget, too, that you have two freebies. Until that third strike is in front of you, you're free to do stuff that you CAN'T drop at a second once a queue pops.
Face it, situations where you can't make it to the queue in time aren't going to crop up very often during natural play. Unless you're a tank (in which case your queue time is nil anyway), you can usually flee FATEs. If you're crafting, even something complicated, that queue needs to pop near the start of your synth for you not to have time to finish. Bathroom break? They happen, but they're unlikely to happen three times in a row unless you're ill or something. Long cutscenes? Yeah, them's the breaks, but you only have to deal with them once each.
For those two free strikes, your playstyle doesn't have to change at all from what it was before, and you STILL likely won't expend those strikes. If you DO expend them, then it is now time to choose your activities more carefully. If you're in duty finder on your third strike, go to the bathroom first. Don't start any quests with long cutscenes. Be cautious about venturing into areas with lots of aggro that you might not be able to escape in time. Keep your crafting simple. Gathering is a good pasttime. And so on. It is not unreasonable to ask players to exercise a bit of common sense when they're on the verge of earning a penalty.
And if you take every precaution and STILL somehow manage to earn that third strike? You're out of Duty Finder for a half hour. 30 MINUTES. Whoop-de-frikkin'-do!
tl;dr, players who play normally will rarely have a problem with the three-strikes rule. People who formerly abused the system will have MAJOR problems with the three-strikes rule - especially if they expend their free strikes to further attempt to abuse the system, leaving them perpetually on the edge of a penalty. And that is all as it should be.