There are two issues. First, they tend to arrive suddenly and ask the player to quickly perform a set of steps they do not often practice and usually lead directly to a fail state. Because of the surprise, this often means players will fail on the first try. The second problem is that it serves as an abstraction of what the player was already doing and effectively seizes player control and removes player agency for a segment of the game. It becomes a cutscene you can fail at.
Heavy Rain was a game that relied nearly exclusively on QTEs for it's mechanical interactions and thus managed to avoid both of these issues entirely. That it wasn't a particularly good game is largely related to the story itself rather than the reliance on a mechanic. This was because the interaction was both expected and because the game made heavy use of this abstract control method throughout the game in the aim of being an interactive movie. Thus it is easy to see that the problem with QTEs is that it effectively serves an interest that is contrary to what most games aim for.
Heavy Rain was a game that relied nearly exclusively on QTEs for it's mechanical interactions and thus managed to avoid both of these issues entirely. That it wasn't a particularly good game is largely related to the story itself rather than the reliance on a mechanic. This was because the interaction was both expected and because the game made heavy use of this abstract control method throughout the game in the aim of being an interactive movie. Thus it is easy to see that the problem with QTEs is that it effectively serves an interest that is contrary to what most games aim for.