I've been pondering, too, the "underneath" for a run. That would be exceptionally unhandy to have to get under there to get a chicken.
I don't think that is too much of a problem. You could get yourself a fish landing net with long handle to reach under the coop. That would be good enough to scare the chicken(s) out from underneath, or you just scoop them up in the landing net and pull them out. Probably easier just to throw some chicken scratch out in the run and they would come out from underneath running to get the treats before their sisters. For the occasional egg that might get laid under the coop. you could get one of those handy reacher/grabber units to extend your reach.
If it really becomes a problem for you, then just block it off. I doubt it will give you that much trouble. Sometimes we overthink the potential problems and forget how often that it is likely to really be a problem that we can't overcome.
Yes, life is easier with a walk-in coop and run, but there are a number of devices you can use to make just about anything work for you. The chickens don't care, so just think out of the box on how to make things more accessible for you.