Immersion heater advice needed

DPinBucks

Dead right, but it's not quite that simple in practice.  Hot water loses heat faster than warm water, because the temperature difference with the surroundings is higher.  A lot of the cost of a hot water supply system is maintaining the temperature of the tank.  So without perfect insulation, it would cost more to keep water at 60deg than it would at 50.  Domestic systems have to be practicable as well as efficient, which is why combi boilers are not recommended for larger homes: they have trouble keeping up with demand for instant hot water.  And a mixer tap allows you to have instant water at any temperature between the maximum and minimum temperatures you're likely to need, between hand hot and tepid.