I imagine this has probably been discussed previously, but why did Renly and Stannis not become princes after Robert seized the throne?

I believe GRRM has discussed this and basically said Robert chose not to, and it was a sign of his lack of attention to the finer details. Especially with a new dynasty, having lots and lots of Princes and Princesses running around would have been a very good thing to show that the Baratheons were here to stay.