I'm not that hard core left or right, black or white.

Onchain are my life savings, in cold storage own keys.

LN is my wallet, I have a few months of expenses in it, mostly due to value increase while it was on LN.....

For daily expenses I wouldn't mind too much if it was self custodial or not, but I use a self custodial one since I put some value in it.

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No I understand that.

I was referring to the enforcement of actual supply of BTC on L2 being possible only if everyone is using self custodial.

Otherwise there could be rehypothecation on L2 by banks.

To be honest I thought also Lightning does not enable to create 'new' or additional Bitcoin ?

Even non custodial, some party had to make all #Bitcoins on LN available by temporary lock them onchain.

Again as far as my research went...

Yes, you're right. LN itself does not allow it, But the only way to verify whether your LN Sats are real - is to run a LN node/channel yourself right?