It is true that heat pumps coefficient of performance drops as the output temperature increases. So you need a proportionally larger hot water tank to store the same amount of energy. So it is fair to say there are tradeoffs. But hot water storage is still a necessary part of most heat pump installs - because peak output of heat pumps tends to be below the heat demand of showers.
You're right, of course heat pump water heaters use tanks to smooth out DHW demand, but that same thing isn't feasible for space heating.