Isn't there just an unbalanced hot water only solution ?

Yes. I installed such a system in my last house. It is called a single
impellor pump. I had mains cold to every outlet and pumped hot to my bath
and shower only. I decided not to pump the kitchen as the flow was fine
there (due to the much greater head) and I didn't want the noisy pump going
off at night just because you turned the kitchen tap on.

Obviously, you could also install a Megaflo, if your mains are good enough,
and your wallet thick enough.

Christian.