My, maybe nieve, understanding is that the pump will balance the flows
and prevent any temperature fluctuations due to surges etc in either
the hot or cold supply.

There are two types of automatic valve commonly found in shower mixers. The
best mixers have both types of operation.

The pressure balancing type ensures that the water pressure is identical for
hot and cold. It is rapidly responsive to changes in pressure caused, for
example, by taps/toilets being used elsewhere.

The thermostatic type measures the temperature of the outlet water and
adjusts the flow of the hot or cold accordingly. The response is much
slower, but it enables an exact output temperature to be set regardless of
the temperature of the hot and cold water supplies, which may fluctuate over
time. This means that you don't have to adjust the mixer several times
during the shower.

I would only buy a mixer with both types of operation, even with pumped
operation. I would also ensure that there are independent temperature and
flow controls, with the temperature graduated in Celcius. Some types have a
single control, which is hopeless, as you lose the temperature setting every
time you turn off and the flow is often too strong to be comfortable.

Christian.