I feel the same way exactly. I admire the craft but I don't want to spend time with it. Logic puzzles feel like work after a while. I like games I can play imperfectly.
It’s not a puzzle in one critical sense: there is no single set solution to each level. I would say it’s an abstract, discrete (both turn- and grid-based) strategy game.
I think it's described as a tactics game, to emphasize decisions at the micro level, as opposed to a strategy game which usually is larger in scope and encompasses things like base building and resource gathering.
It's a tactics game with perfect information and deterministic actions, which transforms it into a puzzle game if you are inclined to treat it as one. The fact that some puzzles may be unsolvable is incidental (and usually avoidable, if you solve previous puzzles well).
For some people, the puzzle aspect is where the fun is. For others, it's a recipe for frustration.
You can say that because we don’t have an agreed definition of a puzzle game. For me it’s as much a puzzle as chess or go, which is to say it isn’t. For my definition having only 1 intended solution is what separates abstract strategy games from puzzles.
I enjoyed it a lot. In the harder difficulties I sometimes would spend 15 minutes planning many moves in advance, and it felt rewarding when you crush the game by doing so.
But eventually I grew very tired of the mental effort required. After a long day using my brain, doing it for fun was just not doing it for me anymore.
It's similar to a lot of Japanese "tactics" games in that regard (eg, Valkyria Chronicles). Games which have a lot of elements which make them look pretty free-flowing, but the scenarios end up being rather strict puzzles.
I’ll say that Into the Breach was what I had hoped FTL would have been. But I don’t like rogue-likes and love puzzles. (I suppose logic puzzles were more like what work was instead of debugging AWS configurations…)