Bathroom hot water mixer tap slow because of mixer tap design? Is pump necessary?

Not knowing what type of hot water system you have, I would assume it's a hot water cylinder, so therefore its gravity fed. Often we find that modern mixer tap design have much smaller flexible tap connectors restricting the flow rate, especially the hot water, because you cold water is mains fed this tends not to impact much due to the higher pressure of the cold water. Either you change the mixer tap for one that has a better flow rate or fit a booster pump to your hot water circuit, this can be costly!