In the case of turbocharged engines the free flow of exhaust gases promote rapid acceleration of the turbo resulting in faster build up of boost.
Cast Turbo Manifold
Any restrictions here will result in increased turbo lag and possibly high speed power loss, due to a smaller turbine housing used to accommodate the limited flow.
Improvements made in the exhaust manifold can significantly influence the power curve and the “feel” of the engine, that is, how it responds to the driver input.
This is especially true for factory turbo cars, where the typical design, due to cost, complexity, noise, emissions, etc restrict exhaust gas flow resulting in inefficient power.
A good example of this is the Toyota Supra exhaust manifold, which is so tiny in dimensions, that it significantly impedes exhaust gas flow. An upgrade to an aftermarket tubular exhaust manifold provide significant more power across the power band as well as improves turbo spool, effectively decreasing lag.