That's a good point. Keep in mind that there weren't all that many aristocrats, and they tended to go into the army. That changed around this era, where younger sons were sent into the navy (like the Duke of Clarence). Still, there were a few there. The Earl of Northesk, Lord Henry Paulet, just to name a couple. As for Granger, as his parents pointed out,he's a member of the aristocracy, so he would be more likely to acquire a peerage. Nelson, for example, was the son of a preacher. It's a much longer jump for him. That would explain why Granger may get there as a captain, while for most it required waiting until they were admirals.
You also raise another good point, that being what happens to a son who inherits a peerage? I would expect that they'd try to be posted closer to home, or possibly give up their command and spend their time in the Lords or managing their estate.