Let's take two airplanes:
1) 1320lb gross LSA (100hp)
2) 2640lb gross non-LSA (200hp)
To reduce weight and increase performance, aircraft B leaves two 200lb passengers behind. Aircraft A leaves one 200lb passenger behind. Which one gets the bigger performance bump? Answer: the performance increase on a percentage basis is identical.
It's not about power, it's about power to weight.
Sure, at 10,000ft takeoff roll might double...the same as it does for every normally-aspirated airplane. There's nothing inherently low performance about a 100hp airplane, it just depends on weight. And with wing loadings usually lower for LSA than other GA airplanes, the LSA might actually have an advantage at higher altitudes.
My CTSW breaks ground in about 600ft, and then climbs at 900fpm at gross; if my takeoff roll doubles I'm not going to sweat it on a decent length runway.
Sport Pilot ASEL, LSRI
2007 Flight Design CTSW E-LSA