valve timing

What is the purpose for not having the intake valve closing exactly at BDC and opening exactly at TDC and exhaust valve not closing exactly at TDC and opening exactly at BDC. Its under my understanding that an engine could push the maximum amount of power if the valves were perfectly timed to open and close when needed to fully optimize the engine strokes. Any clarification on why the valve timing is the way it is?

Basically because air movement has momentum, and this is affected by the pressure difference. You need to look at this cycle as a whole trying to maximize the pressure on the piston in the positive rotation direction, and minimize any adverse forces. I think this page has a good description:

https://www.austincc.edu/wkibbe/valvetiming.htm

Thank you for that link! it helped me understand it better,much appreciated