We hardly even used the stroller with my 2.5yo DS in April. Only one day, because we skipped his nap back in the room so he slept in the stroller for an hour or so. It was such a pain to deal with, I was so glad we didn't use it any other days! We might have been able to go a little faster at times with it, but maneuvering it through a crowd and having to deal with the whole park it/find it later thing got old really fast.
FWIW, my ODD did not use a stroller on her first trip at 4yo and never had any issues with walking at all, and it was in the heat of summer. Honestly it just wouldn't have occurred to me to use one with her since she hadn't had a stroller in years by then.
I know some kids will whine about walking a mile even when they are 10-11 years old, but if you know your kid is walking a lot regularly and fine with it, then a stroller really isn't necessary.