There are steps you're meant to go through before and during each move. We were taught "CRAP": you Communicate your move, the opponent Retreats, you Advance / Attack into the now empty space, the opponent Parries "into" the attack, but their body is out of the way. The idea being here that if you forget the choreography at any point, you're still safe, because you can't attack anything before the receiver has retreated out of the place you're attacking. However, the trick is to do this as smoothly and fluidly as possible, because that sells. It takes practice and maintenance not to let the emotion and adrenaline of the scene take over, and stick to the process, while ignoring the muscle memory of the choreo. It's often not considered an important skill during an audition by casting directors or directors, relative to credits and actual acting, and therefore not by actors themselves. Result: dangerous fights.
But cardboard or foam swords? No way. You want the audience to be on the edge of their seats, and that requires metal.
Most acting swords are safe in the cut. That's rarely a problem.
The real problem is the thrust. In order for a sword to move like a sword, it needs to be stiff.
Most fencing/acting swords have blunt/rounded tips, but that doesn't really matter if you get stabbed in the face - there's just too much force over too little surface area and some facial bones are too weak. In order to be truly safe without a fencing mask, the tip would have to be unacceptably large.
I've never done any sort of theater but have done some boxing and kickboxing type stuff. Newbies will often instinctively do what you describe and need to be trained out of it. A more advanced person sparring with the newer person will suddenly stop and make no attempt to get out of the way of an attack which will still not hit them because it was aimed at empty space in front of their nose for example.
I've also found that martial artists are very confident in their aim and control. Actors must not be, because things go wrong on stage, and errors result in injuries. You may be able to stop your punch within 1 inch of my nose 999 times out of 1,000... but I'm not going to go on stage with you to find out if this is my unlucky day.
It's not that martial artists can't be good stage combatants. They just need to step back and relearn everything in a completely different way, rather than adapt what they already know.
I assume it's impossible to do this with sound effects without it sounding stupid (because if not, they'd presumably be doing that). Is there a reason why?