Lyft used to do something similar couple of years ago (at least in Bay Area) in Lyft Line. I believe they had 10 min wait option wherein when you request and wait for 10 mins you'll get cheaper fare. I remember getting 10-20% cheaper fares consistently using that option. I'd regularly take 10 min wait option especially going to east bay or peninsula from SF.
Uber also has "express pool" option (again in bay area), wherein you have to wait for 2 mins to get matched.
As a rider, these options are great. However, not sure if it's profitable for these companies. I guess with higher rider/driver density, they can make it work?