Is he getting all the opportunity for water he wants? Eats wet or dry food? If he eats dry and has limited water, that may be all that reaches his bladder.
It sounds like he gets plenty of opportunity to go. My boys usually go 3 or 4 times during a walk, less each time, till they seem empty (like your morning walk).
Just be sure you are giving him good opportunity for water, and walks long enough for him to 'pee and re-pee'. Not emptying the bladder can cause sediment to stay in the bladder, which can then be irritating.
Some dogs just don't drink much, therefore don't pee much. If your vet says he's fine, don't worry! We have a friend whose boy sometimes will only pee once a day, and he has free access to house and water, is very healthy, gets taken for walks…just doesn't seem to need to pee.