I'd actually worry about crowding skies above the planet. A rocket flying with suborbital speed has arguably less means to avoid collision if the possibility is detected in flight. Also rockets will need to pass heights where lots of satellites, orbital debris and even charged particles can present some danger to flying objects.
Also, you can design flight paths so they never intersect unlike aircraft that need to deal with weather.
By a hell of a lot – concorde is an order of magnitude slower than the spacex solution claims to be, only ~2000km/h