No. It would break the core design of the game in many different ways. This game was simply not designed to be played without the time limit. On the other hand, you'll get access to a New Game+ mode that eases the pressure somewhat.
The time limit is going to be generous enough that you shouldn't have to stress out over it, but tight enough that your choices should feel meaningful.
Instead of comparing what I'm doing in this case with poor implementations of the concept, have a look at the primary inspiration behind the game mechanic: The Persona series. It is built around having not just one, but several time limits you have to deal with, and it works exceedingly well. Those games would suck if you somehow could remove the limit without breaking the game (you couldn't since it's so intrinsic to the design, but whatever).