With United Airline's Basic Economy "N" class fares, carry-on luggage that goes into the overhead bin is not allowed (mostly). Basic Economy passengers who bring a carry-on to the gate anyway are supposed to be forced to check the bag, and fined extra for it.
So if I purchase a more costly fare that is supposed to include one carry-on, but then I am forced to gate-check my carry-on because the plane ran out of bin space, then I am essentially being downgraded to a lower class of service.
Am I entitled to a refund of the difference in fares? Certainly if I had known that I would be denied a carry-on when I booked, then I would have purchased the cheaper fare in the first place.
United could (but probably doesn't) sell more N fares and less of the other economy fares to control the number of carry-on suitcases. In other words, the airline has the ability to not oversell the bin space.