Would there be any benefit in leaving the puppy with its mother until 12 weeks even if its littermates are sold at 8 weeks?
I want to pay an extra fee to the breeder so he keeps the puppy an extra 4 weeks.
Yes. Dogs develops their "dogginess" with their mom and brothers. They learn what a correction is, how to behave in a hierarchy and every piece of social interaction with other dogs.
This learning can be stretched up to 5 months, where the puppy will learn a lot more from their mother, like orders, routines and even jobs she makes.
This is one of the biggest problem with dogs in our days. We humanize them A LOT but they don't have a "defense" against that because we took them apart too soon from their families.
So yes. I think you are making a correct assumption here. 4 weeks, in a good condition, will make him more stable, and likely he will have a stronger behavioral base to start with than his brothers.
Here and here you have some numbers. You have a lot of studies to look at. I personally worked in a study over a work lineage of Belgium sheperds. Maybe I have been too simple in my answer, leading to that "opinion based" comment. Sorry.