the oil pump simply pulls up and moves oil, its pressure is regulated by the relief valve built into the pump, its the small piston/bush with a strong spring under it.
When the oil fills up the galleries, oil pressure pushes this piston back opening up a relief port dumping oil back into the sump. ergo thick oil cannot damage a pump, only dirty oil damages a pump because the oil pump circuit only has a strainer, the oil filter is after the pump.
Now comes the point of flow vs pressure - cold oil is thick and has high pressure but low volume of pumping vice versa for hot, an everyday example is your garden water pipe/hose, open the valvetap and water your garden.
In this example
watertap = oil pump
you = pressure regulator
water = oil
if you pinch the end of the pipe, you will see low volume output with high pressure, but if you let it flow with no restriction, you see high volume supply with low pressure.
The requirement depends from engine to engine, some have hydraulic tappets and need a quick large supply of oil for them to pump up and stay pumped, (infact thick oil can even cause valve float in those engines) And if you see restrictors in the main oil galleries DO NOT TAKE THEM OUT, they are put in for a purpose - to regulate flow to certain parts of engines, classic case of failure is Honda A16, D12 engines, Mitsubishi 4D55, 4D68, mazda E (808, 323 etc), daihatsu CB23 - 90% of mechanics used to throw out the tiny orifice jets in the blocks, they were to ensure high volume oil supply to the crank. Mechanic ustaads used to throw them out when rebuilding as they would be partially clogged with sludge, and they could never understand why oil was being forced through those tiny needle width holes.
So stick with what the manufacturer tells you, they built the thing, not kallu, nanna, babbu, pehalwan, cheeta, ustaad etc.