I wouldn't blame the overlap as much as duration. The less the valves are closed, the less time available to extract power/work from the chamber pressure.
If the intake valve closes well after bottom dead center, at low revs there's less pressured/density to compress. Effectively a "lower dynamic compression". This helps reduce pumping losses at high rpm, but without more static compression it makes the engine super soft down low.
Widening the lsa doesn't help this one bit. Advancing the **** out of the cam can though. There's still some loss of power extraction because the exhaust will open sooner but the gain in "dynamic compression" is usually better than the loss of work extracted by the piston due to the early exhaust. Getting the right static compression is even better.
Overlap, or a narrow lsa, can actually get gain back torque below peak due to the supercharging effect it can create. Of course, too much of a good thing is a bad thing too.
An engine needs to be built for a purpose. That purpose needs to be well constrained, and then from there the cam and heads and exhaust can be put together in an intelligent manner. Throwing "torque parts onto torque parts" doesn't go very far.
