Telika: Important it is. It would feel as pointless, and as a false promise, to invest time in a long doomed run. I just don't like playing against loaded dice. It's also why I don't like long RPGs where you can realise at the end of the game that your build had no chance of success (typically, the skill points in diplomacy, barter, stealth, swimming, waiting, painting, smelling and nail clipping turning out useless in a last sequence that absolutely necessitates maxed-out swordfighting and translating).
dtgreene: Would you have the same issues if the games were short (like, say, a complete playthrough being a half hour or less)?
Not as much. That's why I specified "long", realising there are cases of impossible short runs that don't bother me much. Solitaire card games are an exemple. The goal is to explore whether you've been dealt a win combination or a lose one.
But still, it's a matter of degrees. I prefer Freecell to Solitaire because success in Freecell depends on me (there's only a couple of unwinnable card deals in the immensity available). A short unwinnable game is still a bit of a flaw, to me. Like a labyrinth generator failing to build an exit (or a roguelike that walls some stairs out, with no possible devices allowing to reach it). If I get an impossible situation in a short game's random map (say, in some "Into the Breach"-like or "Desktop Dungeon"-like), I just go "oh well", and restart, with the vague impression that it hasn't been thought through thoroughly enough by the devs. But I prefer having faith in the fact that any presented puzzle is solvable and therefore is actually a puzzle.
It's also a matter of announcing it clearly. A "mate in 4 moves" exercise would annoy me if the answer is "you can't, lol". But if the question is "can you ?", then why not trying to find out the answer. But this has to be the purpose. And most games (with unsolvable seeds) explicitely demand "do it" instead.
I also make an arbitrary difference between unsolvable seeds determined at the start of a long game, and an unsolvable situation determined by some randomozation at a later point. FTL can throw me into a deadend situation, okay. If that deadend situation is pre-determined from the start, it irks me much more. Mathematically, there's not much difference between both situations (and the difference is invisible anyway), but cognitively it changes everything to me.