This is how chicks learn social behaviour and pecking order and respect. Far better that they learn it under the protection of their mother than once she has weaned them and they have no support.It's best to do, so the chicks don't get picked on by the other chickens. Also, it ensures that the chickens won't eat the chick feed.
Chick feed will actually benefit the whole flock at this time of year when they are moulting and need a little extra protein, but I use a "creep feeder" (my bottomless cage on bricks) for the chicks' food normally.