Re legionella, our heat pump system does a boost cycle for the HW cylinder once a week – heat pump on full, boosted by immersion heater to hit 60°C for an hour.
Re running costs – based on some rough assumptions about our old gas boiler (non-condensing, so not very efficient), estimated CoP for heat pump, and cost of gas vs electricity and looking at historic gas usage, I concluded that the combination of losses in old gas boiler, and CoP for heat pump would roughly match the multiplier for cost of electricity over gas (per kWh) – i.e. actual running cost likely to be similar.
The fact we had to upgrade loft insulation to qualify for the grant probably improved the numbers somewhat. Capping off the gas and hence saving the standing charge also helped a bit.
If UK retail electricity costs ever reflect the generating mix, rather than wholesale gas price – the running costs might start to look better.
We had solar panels & battery storage fitted just before the heat pump, so our actual bills have dropped – but that required more capital up front. We are quite lucky with the roof orientation, so the solar does make a big difference.