We cannot have frequent stops on a high speed single track line, just as you cannot have express trains on a local track.
The British ran 'slip coaches' for 100 years, where they'd uncouple a single car from a passing express train, letting it roll into a local station with a skilled brakeman. The coach would then hook up with the next train that actually stopped at that station.
The British never managed to make a motorized slip coach that could catch back up and recouple with the parent train. This would have made a continuous express train looping the country possible, with passengers coming and going via a sporty self-powered railcar. These railcars exist worldwide in electric, battery-electric, and diesel versions, and are used used in Oregon for the Westside Express Service line between Beaverton and Wilsonvllle, but not in a version that serves as a shuttle to and from passing express trains.
Single-pod hyperloop designs that allow small groups to ride directly from point to point with just a couple minutes of airlock action of each end may be technically feasible, but if it sounds too expensive, it probably is.