Future self custody road block?

Bitcoin has a current daily transaction limit of approximately 500,000 transactions per day. I have heard there is a theoretical ceiling of about 2 million transactions per day. Maybe these numbers are off IDK? Please let me know

I believe that off chain and layered payments can solve most or all of bitcoins scaling issues. The issue I see with a total daily network transaction limit of a few million a day is self custody would be almost impossible for a large amount of people. If there are 8 billion people that want to do on chain transaction that leaves 1 transaction every 4000 days per person. It is unlikely every person will want to do that so let's say 1 billion people would like to own Bitcoin in self custody. Each person would get to make a transaction once every 500 days to a cold storage wallet if that was all the network was used for.

This would make controlling private Keys be impractical for most people. I believe Bitcoin is the future of money regardless but I'm curious how this problem will be solved. It seems likely in the future that possiblely the only people doing transactions on chain are from huge institutions like banks nations states corporations etc

Thoughts/criticisms tell me why I am right or wrong