The time limit is intentionally not in SRB2.
The simple reason is that the last thing you want to do to the player when they're lost is to add insult to injury by killing them. If the player knows where to do, the time limit does nothing, and if the player is lost and frustrated already, THAT is when it triggers. Also, some of the single player stages are definitely large enough to encourage the player to explore, and I see no reason to arbitrarily restrict the player to 10 minutes exploring when they can easily spend a half an hour scouring the stage for stuff.
The reason behind the 10 minute time limit in the classic games is because it is possible to get stuck in the classic games because of occasionally shoddy collision detection. The 10 minute time limit allows the player to at least have a method of getting out if they somehow get stuck inside a wall.