They says that for leases, the 'pay per year' method is cheaper, but let's boil that down.
On a three year least, with the 'pay per year' method, you'll pay $0 for your first year and $80 for each of your next two years. So $160 total.
If you leased the car with the one-time $300 fee, you don't pay $300. You pay Sales Price minus Residual. And the residual on some of these cars is up to ~60% of sales price. So lets say that the residual on a BMW is 58%, that means Car Play would have cost you $300* 0.42 = $126! Still cheaper! You'd have to have a residual less than 47% for the new method to be worth it.
You are assuming that the CarPlay license is part of that residual. Is CarPlay transferable to the new owner? Are you sure the "remainder" of the CarPlay fee goes into the residual value? I expect CarPlay is outside that residual. The residual is supposed to be the wholesale value of the car. If CarPlay is not transferable it can not be part of that value.
Right now it absolute is part of the residual. Right now in BMWs, CarPlay is an optional feature (despite that on most other cars CarPlay is included as a standard feature). Think of it like an optional sunroof. The leasee pays part of that cost just like he pays for part of the car in general.
My current car has CarPlay. If I sell the car to someone else, she gets CarPlay, too. Just like she gets the sunroof I paid extra for. It's part of the car. CarPlay isn't a service (like satellite radio, for instance). No one is coming to lock the sunroof shut in my car when I sell it. BMW will lock CarPlay, though.
No one else charges a yearly fee for CarPlay. My wife's near-poverty-spec Honda came with CarPlay, and it'll work years down the road even though we don't pay Honda anything for it.