From an opposing view as devils advocate what your suggesting could potentially hurt the ones who died during the fight if they die early on in it and no-one resurrects them which happens very often including a lot of the time not resurrecting after fight too so need to re-spawn else their reward and contribution is tiny, or the fate is one that moves around so they end up outside the area laying there dead. Keep in mind these are people which during a fight they helped contribute to in most cases get you through it whether in a speedy fashion, get through it partially or get through it at all. It would be a bad idea to lose all your progress by stepping outside of the area of the fate because fate areas are typically VERY small and it is sometimes far too easy to step outside by accident.
One other thing, most people do not run out of a fate on purpose to reset unless they are about to die and no-one there cares enough to heal them in the first place, if they are tanking it and are about to die hence try to run then maybe someone should heal them, if a DPS or healer gets it then maybe a tank should pull the mob off them but you cannot expect people to always die just to serve your needs. You could always make a fate party of your own if want people to do what you want and come to an agreement with them prior to starting instead of just expecting everyone else to do what you want based on nothing more than your own assumptions that they would.
Remember this...these people are not here to serve your needs, the world does not revolve around the fates you want to do and they are under no obligation to help you do a fate anymore so than just because you want to kill an S or A rank mob does not mean everyone has to come to you and help you kill it. If they got you 50% of the way through the fate, that's 50% more than you might have got if they were not there.
Unlike a dungeon in which people agree to do something prior to starting it which should carry through on what agreed to doing when accepting the commencing window...with exception of emergency cropping up forcing someone to leave or an agreement made within the dungeon that you could leave for non emergency hence vote kicking and vote abandon and 30 minute penalty if do so without either of those previous things. The fates are open to all, free for all to help or not help as they see fit, do the ones they want and not be forced to do ones they do not, there is no agreement or promise made to you prior to starting that they would help you with the one you want until it ends, no agreement forged by having to do ready checks or make a promise by way of a popup window that gives them one final chance to back out before beginning.
By the way I will mention that I never leave fates unfinished unless I keep dying and no-one is helping or it is not possible for me to finish but I have no intention of demanding everyone else has to be forced to help me finish any I chose to start doing. Worthy of note also is no-one forced you to start a fate that you would not be able to achieve alone. You chose to do a fate that relies on others despite no-one agreeing with you to stick around, you relied on the charity of others but also just assumed that they are there until your needs are served.