I don't think this should apply with Mythos cards, my reasoning being the following: in addition to the extreme power of the ability, in two-player and frou-player games, the clock will always strike midnight on the same person's turn. Thus, the usefulness of Kat'e ability will vary massively based on where she stands in the turn order. And that just seems ridiculous.
There are a number of effects that advance the clock outside of the end of the player's turn. Her ability will come into and out of play during Mythos resolving more often than you'd expect, even with 2, 4, or 8 players (yes, the advances are mostly on monsters, but monster can come out on other player's turns, as the result of terror results, or if she isn't the player making it strike midnight).
As for "overpowered in single player", I doubt this would come to be the case. Keep in mind that she's giving up other abilities, some of which could be even more useful (Sister Mary's ability, in particular, since it means that no dice would be locked for the entire game...). Monsters, at most, make things only slightly more difficult, while providing their own rewards (clue tokens, trophies, whatever).
All of the abilities are rather powerful. Some of them (extra items when taking items) are less powerful in a single player game, but are still good. When you have one power, you don't have the others, which might have been more useful.
And, if you think one power is too powerful, just don't use that character in solo play. Or at all.
I don't get the impression of lack of playtesting. It's a solid game. There's variables that come up in play, but those are largely a part of the game. There are some sections in the instructions that could have been written a little better, but there's nothing major.