It seems unnecessary to ban an entire way of bowling instead of just not allowing people to roll the ball.
Underarm bowling was banned after the incident of rolling the ball which occurred in the match between Australia and New Zealand on 1st February, 1981. New Zealand required 6 runs off the last ball to tie the match. Australia captain Greg Chappell instructed the bowler Trevor Chappell to deliver the ball underarm(which was legal at the time). Trevor Chappell delivered the ball by rolling it along the pitch so that it was impossible for the batsman to hit the ball for a six.
Underarm bowling was banned by ICC as a result of this, as it was considered to be not within the spirit of the game. However, underarm bowling is allowed if it has been agreed so by both teams before the match.
A delivery bowled is deemed a no ball if it rolls before reaching the popping crease as mentioned in Law 24 of the Laws of Cricket.
Law 24: (emphasis my own)
- Mode of delivery
(a) The umpire shall ascertain whether the bowler intends to bowl right handed or left handed, over or round the wicket, and shall so inform the striker.
It is unfair if the bowler fails to notify the umpire of a change in his mode of delivery. In this case the umpire shall call and signal No ball.
(b) Underarm bowling shall not be permitted except by special agreement before the match.
- Ball bouncing more than twice or rolling along the ground
The umpire shall call and signal No ball if a ball which he considers to have been delivered, without having previously touched bat or person of the striker,
either (i) bounces more than twice
or (ii) rolls along the ground
before it reaches the popping crease.