Severe limitations? They were able to fly higher than other planes. When an aerial engagement starts, the plane with more altitude usually wins.
(Altitude=energy)
They flew higher than
some, not all -- if we're comparing models of the same year. If you're comparing a latewar 109 with something from earlier in the war, its performance will of course appear better. The only folks who built planes that had consistently low operating envelopes were the Russians, as the air war on the eastern front seldom went anywhere near the 109's maximum altitude...which meant that in that case, the compromises made in the 109's design to get it flying high were of no value at all.
(Interestingly enough, the Russians respected the 109 for its agility and scoffed the FW-190, while western pilots had pretty much the opposite opinion in most cases. One of the reasons why I enjoy these discussions are that there are no correct answers.)
Engine stalls when diving will kill you if you are trying to extend from an enemy plane. (a classic defense - hit the deck and try to outrun him)
High-speed tactics are pretty much all anybody uses now, because they'd black out otherwise.
Nobody flies the sopwith camel anymore..
Simply pushing the stick forward hard would result in a dive and possibly stall a carburetted engine. Performing a split S would get the plane diving more quickly, vastly complicate accurate shooting by the attacker, change direction, and not stall the engine. The split S is still considered to be a useful maneuver for disengaging today.
Looking over the next generation of fighter aircraft in development or recently completed, we see maximum speeds no faster (and in some cases slower than) what came before, but they all seem to feature thrust vectoring, canards, or both -- developments useful primarily for low speed maneuverability. Someone seems to think this is important.