Then every car (and the tunnel itself!) needs to be a pressure vessel and you need oxygen masks if there is a leak. Plus you have to turn every station into an airlock. Depressurizing the tunnel is a lot of extra work.
It might be easier (although not much more sane) to have two large ventilation systems for the tunnel. One working at high negative pressure (near vacuum), and the other working at a high positive pressure. The vents would be shutters that could be opened and closed rapidly, so you're always pulling air from the front of the train and introducing it behind the train. Basically you would always have a strong tail wind, reducing the heating effects of compressing that much air. The energy required to move the air would be substantial though, and it might not make sense. The high speed shutter system would be relatively complex too, and making it reliable would be a challenge.