Chainring wear to the point od slippage does happen, but it's a long slow process. It's more common on mtn bikes than the road, especially on the middle ring. (the granny fares a bit better being steel, and usually used less).

Unlike cassettes which may slip even when they look pretty good, worn chainrings usually have visibly shark finned teeth, and are obviously worn looking long before they slip.

One test to predict slippage is to pull the chain out from the ring at the front (1/2 way around the wrapped side). If you can pull the chain out so there's almost 1/4" gap underneath, get out the butter because it's toast.