The Las Vegas tunnel is 12ft diameter. The London Underground deep-level tube diameter is 11ft 8in. Underground is considered too small but is possible to run trains in tunnel that small. Plus, Las Vegas doesn’t need heavy rail but some light rail or pods would work well.
Trains tracks tend to be designed so that the trains must stop at each station, something that can add plenty of time to a trip. Ideally, the smaller cars/scooters/whatever can load and unload out of the main pathway making it possible for every trip to be non-stop.
The actual practice behind metrorail and PRT operation, not to mention the actual operation of the system here, puts some lie to the theory you're working under.
When you design a system so that vehicles have to shunt to and from a station, you strongly limit the capacity of the system by that shunting system. Unbranched metrorail lines can reach 45TPH in normal operation, while branched lines do worse, and systems with heavy reverse branching (splitting from one line to rejoin another, NY's and DC's systems do this something fierce) struggle to get 24TPH. PRTs get better headways because they're smaller vehicles, but they're not really any better than a standard highway lane in the best case (which is beaten out by just about any other rapid transit system in existence).
If you look at the station design here, it's phenomenally bad from a throughput perspective. They appear to be using low sedans (which mean people take longer to get in and out of their seats compared to typical trainsets or buses). Furthermore, the parking spots are angled parking, which requires the cars to back into the travel lane to exit the station, backing up even traffic trying to "express" through the station. There are honest-to-god traffic jams on this system at even moderate capacity events. (Compare this with subway stations, where the station being at crush capacity utilization leads to trains skipping the station until it clears out; that's harder to do in this system.)
Currently living in Switzerland, here they just use railroad switches. So express trains can run uninterrupted while e.g. another train is on a separate track in the station.
Uh, it's not about the passing lane on the road. It's about the station. The passing happens at the stations. The car gets out of the way while people load and unload. That's the ideal design.
Sharing a train or bus just forces everyone to stop at everyone's stop along the way.