Hi Nigel,
I hear what you say but :-
1.  I'm thinking that if a 30m green hose pipe gives me about 10 litres of water hot enough for washing up (and too hot for showering) then 100m of black 32mm pipe would give a lot more (i.e about 300 litres).  More than enough for general houshold use at any one time as once you've done the washing up or showered (or whatever) the residue in the pipe would carry on heating up.  It wouldn't be difficult to locate the pipe in the lee of the wind ?
2.  See above.
3.  Don't get that ?
4.  Ratio mentioned in 1. still applies.
5.  Ratio mentioned in 1. still applies.
6.  How much washing up etc. do you do at night ?
I'm not trying to deliberately contradict you and your laws of physics are correct but it seems to me that it would be very cheap and simple to construct.  I'd give it a try if I had nowt else to do and a 15€ bottle of gas lasts about three months on the water heater.
Could an insulated storage tank not be included in the circuit so that there was a resevoir of pre-heated water to feed the boiler in the morning ?