One thing to consider with 'instant' heaters is the max hot water flow rate. ie ambient +X degC litres/minute.

The main problem is that to run a decent shower or fill a bath in a reasonable time you need many kW of heat to be transferred into the flowing water to raise the temperature. In the UK you'll typically be limited to about 3kW for an electric unit.

In the winter this equates to a lukewarm trickle from the shower

Gas of course avoids this problem and some 'instant' heaters and combi-boilers actually have very well insulated tanks built in - not as big as your traditional tank but enough to smooth out delivery. Also, IIRC, look up plate heat-exchangers; I think they provide a very compact way of heating flowing water.

Oh, FWIW I understand that washing machines are better served by a cold water feed.

The logic goes that they use so little water in real terms that by the time the pipe run has been flushed and some hot water trickles in then the tub is full and you just have a hot pipe run. Additionally they now run at much lower temps. All told it makes sense to just use a cold fill and let the internal heater warm it up.