If they pick randomly, there's no benefit to switching. No harm either.
If it's random, 1/3 of the time you're right on your first guess and switching doesn't help. 2/3rds of the time you're wrong - if the host knows and deliberately doesn't open the door showing the car switching means you win. If however he opens randomly, half of those cases show the car and you can't win - so the breakdown is 1/3 switching wins, 1/3 switching fails and 1/3 the car is shown and you lose regardless.
If it's random, 1/3 of the time you're right on your first guess and switching doesn't help. 2/3rds of the time you're wrong - if the host knows and deliberately doesn't open the door showing the car switching means you win. If however he opens randomly, half of those cases show the car and you can't win - so the breakdown is 1/3 switching wins, 1/3 switching fails and 1/3 the car is shown and you lose regardless.