To explain further, V1 means they cannot stop in time if anything happens. Therefore they must commit to taking off. So why wait for a positive rate? Shouldn’t it be retracted as soon as they see a difference in altitude? From my understanding, is that the landing gear deployed during a crash landing can rupture the fuel tanks??
V1 is the speed at which you are committed to take-off, it doesn't mean you are off the ground. You can't retract the gear at V1 because you are still rolling on it heading down the runway.
Vr is the speed at which you rotate the nose up to get into the air. Again you are still rolling down the runway with your nose in the air, you can't retract your wheels if you are using them.
V2 is the speed at which you are able to climb with one engine inoperative. It doesn't mean you are in the air yet, you can't retract the gear.
And just because the main gear come off the ground doesn't mean a gust won't push you back down, so usually you leave it down until you are reasonably assured that you won't touch again. It's a lot gentler on the aircraft if you touch the wheels than if you rub the skin off the aircraft. Positive rate is pretty much the only indication of this since there is a little bit of a lag in the VSI, by the time it shows positive rate you are far enough off the ground that you really don't need to worry about touching again.
Shouldn’t it be retracted as soon as they see a difference in altitude?
The best indication is not the altimeter, it is the VSI. It reacts faster than the altimeter.
For GA aircraft, a lot of pilots won't retract the gear until "there isn't any runway left". This means that taking off on an 8,000 foot runway, they would be airborne by the 1500 foot mark and leave the gear down in case the engine fails they can just put it back down again.
What you really don't want to happen is for the gear to be retracted prematurely. When you are rolling down the runway you get "light on your feet" and the gear retraction mechanism can pull the gear up before the aircraft is ready to fly. The squat switches may be unloaded so they won't stop the system. Best thing to do is to wait for the positive rate, verify visually and then retract. Personally I leave it down until I'm 500' below pattern or no more runway left.