I know that most of the players (except maybe 1) would be pretty disappointed if they didn't get to act in the combat.
Alright, I grant that that would be something that could apply to the PCs. On the flipside, combat is dangerous and difficult, and an expenditure of resources.
Not having to spend those resources is a boon;
not having to take risks is beneficial.
There's also something to think about, in terms of frequency--"sometimes go[ing] 5+ sessions without a combat" could mean anything from "this happens fairly often but not all the time" to "it's happened more than once in 10 years of play." Given that we're already talking about
another relatively-rare event, PCs doing so phenomenally well that they defeat a big enemy (or full party of smaller enemies) before the end of the first round, such an intersection of at least an uncommon event with a very rare event should be even rarer--rare enough to be not really worth worrying about in the grand scheme.
Speaking as someone who's never DMed, I usually feel rather relieved when combat ends. There might be a twinge of...feeling miffed, I guess, that I had an idea or whatnot that now doesn't matter. But it doesn't matter because my allies were FLIPPIN AWESOME, not because I did anything wrong. Any negative feeling on my part will be completely overwhelmed by congratulatory feeling for my fellow players--the dice were with them, and they totally owned whatever we were fighting.
Which is part of why I find it a little hard to believe that the
players are going to feel particularly "embittered" about not getting to act. If the player doesn't get to act because her allies already ended the combat, that seems like a generally
good thing. She'll have other chances to face death bravely, for now she can take heart that her allies are strong (or lucky!) and therefore good to have around. For me, the bitterness would make sense if instead I had been
robbed of my action while the combat continued. Few there are who delight in being stun-locked, mind-controlled, etc. for a whole fight, and therefore having a bunch of opportunities noticeably pass them by while their friends suffer. But that's a very different situation from never having the opportunity at all, because success landed in your party's lap unexpectedly early.
I guess...it just sounds...petty and petulant, to feel "slighted" or "denied" by your friends' good fortune. Looking a gift horse in the mouth because it's
chestnut and everyone knows your favorite coat is
palomino, that sort of thing. It's fine to have some mixed feelings, I suppose, but "embittered" sounds
way too strong for "that was super cool, and I'm relieved it's over, even if I didn't get a chance to help."
Of course, depending on the circumstances, I might also just throw in a few additional monsters.
Which sits much better with me than adding HP, if there's a modicum of in-world justification for their appearance. E.g. the party hasn't destroyed all of the golems defending the evil wizard's tower and some heard a commotion; the party tried to avoid alerting the noble-but-misguided guardsmen of the castle; the dungeon is infested with the kinds of creatures that like dungeons, and many more live there than the party would ever clear out; the shadow-druid keeps her forest well-stocked with creatures of death and darkness that could prowl through at any moment. Etc.