Question about lightning scaling back-of-napkin math

Doing some back of the napkin math here. Let's assume a fully bitcoinized economy, everybody uses Bitcoin. 50% of them use a self-custody wallet.

There are 8 billion people on the planet. Let's assume everybody stops having babies and nobody dies for the next 50 years for simplicity on the math here. That's 4 million lightning wallets.

To use a lightning wallet, you must open a minimum of one channel, that a tx on Bitcoin's layer 1. So that's 4 billion transactions.

Let's say that L1 can do 867,000 transactions per day. 4 billion / 867,000 = 4,651 days or 12 years. And that's assuming nobody uses any other L1 transactions for any purpose and that you only need one channel for a lightning wallet, and that channels never have to be re-opened and new channels never have to be made and people never have more than one wallet or have their phone die and need to make another one.

Am I missing something obvious here? Are there any existing BIPs or other proposals to increase the ability to scale?