Old games were like that. Can you remember trying to win Pole Position, Rad Racer, one of those old games, but you had a clock to work with? I mean, you're playing a console, not an arcade. GT with a time limit for a race is like trying to find a girlfriend/boyfriend your age (assuming you're 25 or younger) in a Bingo hall or Polka place.
I say "nay" to time limits, even for demos. And in games like Ridge Racer Type 4, the Time Limit is useless if you're completing a race WELL BEFORE 10 MINUTES.