The thing about limited challenges in games like Card Crawl is that you still have a complete game to play around with. On the other hand, a game that is almost entirely based on timers can at times completely prevent you from playing in any way except through using real money to refresh the timers. I recently tried Pokemon Shuffle, which is actually quite a fun game - when I can play. The game literally limited me to something like 5 30-second matching games every couple hours.
I think that's a useful data point for probing my intuitions, but here's my reason for thinking it's not right: Bonza. Bonza is a sort of crossword-ish puzzle game, which comes with a selection of puzzles, and more you can buy with in-game coins you earn by solving puzzles. There's also a daily puzzle. At this point, I've played all the stuff I can play for free and everything I've bought with in-game coins, so it's basically just a daily puzzle. I find that that doesn't bother me at all. When I've finished the day's puzzle, I have nothing left to do and go on to something else. I think what might be relevant isn't whether there's a full game available outside of the time-limited challenges, but whether the time limits kick in when the game has left you motivated to continue playing. So it's simply a very common special case of the more general problem of manipulative design, where the need to put people in a position to want something they can pay to get corrupts the design of the game. With Bonza, I finish a puzzle and feel like I've come to a good stopping point, and there's a perfectly sensible reason they don't give me another one right away: it takes time to make the puzzles, and they allow users to submit new ones which they then have to evaluate. So it doesn't feel like an artificial limitation they've instituted just to make me pay for one of the puzzle packs, it's just the nature of the design of the game.
The same goes for the Daily Dungeon in Card Crawl. It's not artificial that you can't play two dailies: if you could, they wouldn't be daily. The only thing which distinguishes the daily from the normal mode is exactly the once-a-day format, so it's inherent to the design of that mode, not an artificial limitation. You couldn't buy more dailies if you wanted to, so you never get the impression that you're being manipulated into spending more money.
So my intuition, of which I'm still not confident, is that what makes timers maddening is that the appearance of a malevolent, or at least callously greedy, intelligence behind them. They're intended to cause frustration to make money; it's basically low-level extortion. As such, I think it's reasonable to lump it in with all the other forms of low-level extortion which ruin games for me. Do you feel similarly, or do you think there might be something distinctive about timers which sets them apart from the other corrosive influences on game design, and which I'm missing?