As a Home sustainability assessor, I have seen the energy / home situation many times over the past 6 months.
I have witnessed 2 houses with these Hot water recirculating pumps, and they both had ENORMOUS energy bills- ie 80 and 90 KWH per day for each household .
To clarify- one house was on off peak HW, and that component of the bill was 40 KWh per day! (the other on smart metering)
The other place that had one had an 800 litre capacity hot water (2 x 400 ltr) and I could access the first 8 metres of hot water pipe coming from the tanks. The entire thing was too hot to hold! In both cases, the energy was being wasted to space in vast quantities.
I imagine a much better system is to use small dimension hot water lines- ie 16 mm so small volumes of hot water are wasted, and thick insulation over the entire system would be a better solution. - and get rid of the pump.
Experience shows, many plumbers have little regard for customers energy bills, or any concept of energy conservation principles, so there is little or no insulation on any of the hot water systems mentioned, or most others I have seen.
Any other similar experiences? would be interesting to hear about them....