Here are a few scenarios and assumptions.
1. Eight billion people (and growing) having self-custody and transacting on the Bitcoin Main Chain.
Not possible without major changes on the bitcoin rules and consensus. And making the change to accommodate the objectives is very likely to introduce network breaking bugs and exploits. No one can be certain how things can go wrong. And more realistically, we most likely will never get majority consensus to make such changes.
2. Most people WILL NOT want to self-custody.
If most people WILL NOT want to self-custody, taking the endeavour to change bitcoin consensus and protocols infrastructures and risking network breaking event is totally unjustify.
Can bitcoin still work without everyone taking self-custody and transacting on the main chain?
I would argue, yes.
Current adoption rate is low. No one have problems making on-chain txs and Lightning Network is NOT remotely near to congestions. Thereby, the problem is obviously not now.
What if adoption is high? We posit a scenario where majority of the world is on the bitcoin standard or moving towards the bitcoin standard. There will be thousands if not hundreds of thousands of bitcoin banks running their own Lightning Node, something like Wallet of Satoshi. Where there are many of these LN banks, they cannot really put a wall around it. LN can inter-operate. No one will use one that they cannot go in and out as they wish. Is it possible someone doing fractional reserve? Yes, but they can easily be found out and go out of business. Unlike traditional banks, an LN bank like WOS must have unrestricted in/out with every LN banks, else they will not survive. Countries will be running their own LN network. Private corporation will be running their own network and individuals will be running their own network, all inter-operable.
Liquid Bitcoin while have element of trust will still be there. There will always be element of trust but because Layer 2 is running on Bitcoin Layer 1, users can easily choose who to trust. Unlike now, if you are in any country, you have no choice but to trust the local nation state govt and their currencies. Because we have no choice and cannot opt out easily, that's where abuse, corruption and debasement cannot be mitigated.
Lot's of privacy tech is avail with different trust model. Ecash on Lightning can work in local communities and even global communities with very high privacy.
Imagine, in 20 years time, I cannot or will not self-custody, and I have 100,000,000 sats. I can literally spread them out to 1000 different entities of LN banks, Liquid and ecash banks, all inter-operable and all can easily move around fast and cheap. My wallet automatically manages the funds in the 1000 entities according to my preset percentages, risk of being rug-pulled or frozen by any entities are very low. That's because the 1000s of entities need to compete with each other. The moment any one entity attempt to cheat and being found out, they will go out of business.
The above possibilities are based on the assumption that functioning governments of any kind are in operation. If not, it doesn't matter the protocol changes, you may not have internet access. If functioning governments are competing with each other, and many of them holds bitcoin and therefore incentivised not to destroyed their own value, I think even the current structure of bitcoin layer 2 of Lightning, Liquid and Ecash can go very far. We have not even consider more Layer 2 infrastructure that will be designed. All these without messing with the Bitcoin Main Chain.