It works fine.No they don't. At least not any better than the default rules do. Arguably worse because your adjusted rest schedule is compensates in the wrong direction.
The inn is right over there. It takes them less than an hour to get to a safe place to sleep.
It's not the Warriors where it takes 8 hours to travel from Central Park to Coney Island.
They get humped and walk home like normal people.
If you have an urban adventure, the inn, bastion, temple, hideout, watch house is right over there.
That's why 80% of D&D adventure writers do not write urban adventures. Because it is too easy to get back to the resting place and sleep for days.
There's always some rigamarole to get you out of town to travel for X days so you can't rest and inflate the encounter number.