My four year old grand daughter has gone from balance bikes to normal small bike with pedals and no stabilisers.
We found once she got the balance bike sorted then going to stabilisers was more of a backward step, as it is too easy to lean on one side and rely on the stabilisers.
As her pedal bike was fairly small, then not far to fall and she has hemet, elbow and knee protecters.
Always a worry for parents etc. but she soon picked her self up and no harm done.
When her mum was young I did go the stabiliser route, but this was her choice and I can see it is right for them.