Fate is a resource. If you have a lot of it, like in Black Crusade at higher Infamy+Corruption levels, its an equalizing or high performance tool that you expend to improve your character's capabilities; much like Edge in Shadowrun, saving a few for bad bad times. At that level, Fate/Infamy points are what heroes or archvillains use to nudge themselves into legend.
If you don't have much to begin with, then its a limited defensive measure: something you use to avoid blowing your own arm off because Overheat don't care how reliable your gun is, or to avoid Daemonic Headsplosion chances when rolling on the phenomena table. You keep a tight grip on your one or two little points, as they're your only way out when the dice decide to kick you in the progenoids.
Burning it, well, that depends. I think if a person needs to because of Stupid, that's fine: they've been punished by losing one of the most valuable and limited resources available to a character in this system; whether they had many or few is just a matter of how epic the scale has gotten, really. Stupidity will still send you packing back to The Emperor like you woz painted red anyhow.
For those careful with them normally, even if they have plenty, its a survival tool that will let them survive their character's "worst day ever, again", or give them the edge to survive through the occasional reckless act.
Obviously though, you should be at death's door as a result: Burning fate gets you out of the frying pan, but barely; and if the entire squad went down that way in hostile territory, that might be too much even for fate points. The Black Crusade 10+1d10infamy version does guarantee survival for the session, so that's a good time for captures or "you're okay with <bionics> here right?"… Or the whims of the Dark Gods.
It should never force a downward survival spiral on them though [stuff like "okay so you're back to 0 and they captured you, so you're naked but you get a chance to survive because they throw you into this arena and there's a Krootox on the other side", that's cheating them out of their resource.
A TPK is a TPK, and if from fair and proper dealings, the GM deserves his kill marks.