Cold pipes in the morning is not a water heater problem, that’s pretty typical.
A recirculation pump would definitely work and would have the added bonus of immediate warm water at any time, but it’s going to use extra energy 24/7 to do so–especially considering it sounds like OPs system already has a lot of passive heat loss along the pipes.
Might not be worth the extra cost if the primary problem is just the morning shower.
Cold pipes in the morning is not a water heater problem, that’s pretty typical.
A recirculation pump would definitely work and would have the added bonus of immediate warm water at any time, but it’s going to use extra energy 24/7 to do so–especially considering it sounds like OPs system already has a lot of passive heat loss along the pipes.
Might not be worth the extra cost if the primary problem is just the morning shower.