While Minnie vans are run off of Lyft but they offer many things that Lyft or Uber drivers cant. At Epcot Lyft and Uber pickup is in the Epcot parking lot and they use the same roads as day guests (more on this later). The Minnie Vans pickup up and drop off with the Disney Transport Busses. At Magic Kingdom they drop off and pick up at the bus loop allowing you to avoid the Ferry/bus/monorail trip across Seven Seas Laoon. Studios when completed will be much like Epcot where as Minnie Van pickup and dropoff will be closer. The other advantages are car seats if you need them. The Minnie Vans also have access to roadways and areas that others cant, for example if you are going to Pioneer Hall and Hoop De Doo if you arrive by Lyft/Uber you are dropped off at the main entrance then you transfer to the internal resort bus which stops at all the loops before you finally arrive at Pioneer Hall. Minnie Vans can drive you directly to Pioneer Hall and drop you off right at the Tri Circle D Ranch.
Now here is a personal experience that highlights why Minnie Vans have an advantage on Lyft or Uber. This past NYE we walked out of Epcot at 1:30am and to the bus line for Pop Century. The line was much longer than it was in 2017/2018 and that took us a hour and a half to get back to Pop. While walking to the line CMs were telling people there were no taxis because they couldnt get here because of traffic and the fastest way was the busses. We got in line and I opened the Lyft app and requested at Minnie Van, one accepted the ride and was there in 6 minutes. He pulled up basically right across the walkway from where the end of the Pop line was. We got in and we were off. Trafic was a standstill leaving Epcot and Orange County sherifs had many directions closed and were directing traffic. If you were in a taxi, lyft or uber you were stuck in that traffic. Our Minnie Van was allowed to go down closed roads and backstage areas to get us back to Pop. From the time our driver picked us up we were back at Pop and in bed in 25 minutes. Not to mention, we had a nice quied ride with good conversation, didnt have to stand on a bus, and he dropped us off right at our building. Well worth $35.
Thats why I said for the most part, they get you to the same destinations, just different spots. As for taking certain roads and such, being Disney CMs and not average Joe's they are probably more knowledgeable of the roadways that are available. There are a lot of roads that anyone can access, you just have to know that it's there.