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 Short version is, (much) better privacy, better TPS, lower cost. But there's a ton to unpack here, like what we imagine a bitcoin bank even is. 
 Yea I basically espoused upon that in another comment to this note

What function will a bitcoin bank have for the self sovereign?!

I can’t think of one at the moment 

note1mp2p5ka0f2f3nm6xh7629m0hjz3jmu3u9q9zdv56x4rckdrjdvus5vvmca 
 How far out in the future are you looking? 
Bitcoin self sovereignty does not scale with current technology to the entire world.  
 Lightning won’t scale currently?

If not, what is the max user base on current tech?

(I’m not arguing, simply asking follow up questions)

Also, when you say “Bitcoin self sovereignty does not scale” do you mean the quantity of tokens (ie decimal count)? 
 Lightning works great but if the idea is for each person to be able to run their own lightning node and interact with the lightning network in a self custodial way then we run into problems.
Lightning is still limited by layer one bitcoin. Each self custodial lightning user needs at least one on chain transaction to open a channel and any additional opening or closing of a channel will require an on chain transaction. There are a few problems with this. One is that fees are likely to be far higher in the future making this task so costly it may not be worth it for the amount of funds that most people have. The second issue is blockspace limitations. There is not enough room in bitcoin blocks for each person to have and manage their own lightning channels. Even if the base chain was soley used for lightning channel management it would not be possible for billions of people to manage their channels.

I can't answer what the max userbase could be. It seems to me that the way things are currently going lightning will be a communication or compatibility layer between other protocols like ecash mints, ark, fedimints or even exchanges/bitcoin banks.

To address your second point I am not talking about the number of tokens. There could be 1 bitcoin or 1 billion and nothing would be different.

If you want an in depth understanding of these issues I will link a video that explains it well. I disagree with the title that the lightning network has failed. It is just not the solution to self custody for the masses. 
https://www.youtube.com/watch?v=5Cq0C0SpbkY 
 The idea every person has to have to use non custodial lightning and run a lightning node is ludicrous.