Daycare providers do usually set an age limit on wearing diapers unless the child actually has a medical need for the diapers.
When I worked at a daycare center we had an age limit of 4 years old in which the child had to be out of diapers or at least nearing potty training and wearing pull ups or we would have to terminate the childcare.
In our rooms where the diapered kids were in there was no toilet for the kids so until they moved up to the higher age room where there were toilets then they would need to be potty trained.
We did however make an exception with one boy who was nearing 6 years old who had autism though and we did make exceptions in those cases.
But if the child has no other problems then most daycare centers do set an age limit on when the child must be out of diapers and potty trained at.
Some daycare centers also charge more for diapered kids than they do for potty trained kids.
Daycare centers will not potty train your kid but they will help them along the way.
If the kid however is still not accident free then they must be in a diaper or pull up until they can keep their diaper or pull up dry for a week or two depending on the daycare policy.