3 years old is not too late to begin potty training.
Also 3 years old is not too old to not be potty trained yet as all kids are different and will potty train and stop wearing diapers at different ages.
However once a child gets to 3 and 1/2 then they are usually ready and should begin potty training before the child turns 4 years old.
I would say that once the child gets to 4 years old and above then the child needs to be potty trained even if you have to force the issue.
There are some kids who seem to love to wear diapers and do not mind being wet or poopy and would wear diapers for the rest of their lives if you let them.
But after 4 years old the child needs to be potty trained.
Some kids are ready to potty train by age 18 months and some are ready to potty train by age 2 and 3 years old.