Not going to lie, your friend is probably facing an uphill battle here. 12 direct reports isn't a huge number and your friend's current proposal not only creates an extra layer of hierarchy (which their manager doesn't want) but promoting (or worse hiring) extra managers is going to bring increased costs for the business.
If he wants to successfully pitch this he needs to come up with some pretty convincing reasons why this is proposed structure is beneficial for the business not just him and for why this split also needs his role to continue at the same time. His manager doesn't want extra layers remember - and the last thing your friend wants to do is convince his manager to replace his layer!
If the actual problem is just that he needs his workload reducing slightly because there aren't enough hours in the week then it's probably a better approach to pitch an alternate solution that offloads some of his workload. Whether that's getting him an assistant or deputy, or probably better reducing the overhead.
For example the weekly one-to-ones, say they're currently taking 30 mins each that's 6 hours a week in one-to-ones. Could they be replaced with fortnightly ones instead? Doing this buys him an average of three extra hours a week and an extra three hours a week freed for the team as well.
If the personnel-management aspects are set in stone - then he might have to get creative about other things that are on his plate and see what else can go, whether that's being a bit more stringent on the way other meetings are run or handing off responsibility for one or more of the projects to someone else, maybe one of the more senior engineers.