Considering a majority of the RP is already segregate between social groups, I feel like Sagsworth holds a viable argument. Placing a passive which justifies and wholeheartedly supports private RP will only make the streets feel less lively. Considering most RP is already centralized in passive in bars, work cycles, and whatever the Rebels do.
I've yet to see apartments be used for much. Considering the charge of rent is a weekly thing- it's something I've personally looked over due to that fact. When you're working at a store, if you're not turning massive profits (like a majority of shops), a total of +100c's a week is a bit extensive, and then you split the rent. If you can do the same thing for apartments, I could see this becoming an active and pleasant form of RP.
What would the well rested perk do anyways? Higher XP gain when training skills? Maybe do something that isn't well rested, and instead slows down the loss of hunger and thirst?