The B737-100 used F2 for takeoff, it gave a similar performance as the B737-200 using F5. I used it on the B737-150 a lot (a B737 basic with the advanced wing). I was told it was gated because that was the go around flap setting for the B727 with one engine out and it was easier to set it correctly with the gate than without. For convenience they fitted the same flap mechanism in the B737 when it was first made, as they used the same fuselage jigs etc. It could have been the go around flap setting for the basic B737-100 as well and was left there even after the bigger engines and better performance of the later models because it was easier to to do that than re-engineer the flap mechanism?
It went out of favour when the airlines started using Boeing-generated takeoff charts, for which a great deal of money had to change hands. Having just one or two options for flap settings on takeoff would save a lot of money in chart costs and the bean counters would not know the difference in fuel consumption and cost. However a tail strike due to not setting the correct bugs (thinking you were using the regular F5 and the associated speeds) would offset many years of costs for the fuel savings due to a more optimum flap setting.