I think many airlines (certainly Eurpoean carriers) now have the 2 minutes as a standard, but some will, if asked, take a reduction if the wind is favourable.
It also states in the AIP link that the 2 minutes is a rotation to rotation time. So you will be cleared for take of after between 70 and 90 seconds depending on how long we think your take off roll will be.
How many times have you been asked for another 20 seconds and you end up with a gap of 2.20?
That's something else that differs. In the US the time interval is from start of roll to start of roll. Lots of room for less than 2 minutes there.