yes, this is an issue with custodial lightning as well. At least in this case you design it so that you can easily take custody of your funds using LSPs.
Discussion
I don't know. This seems too dangerous. For me personally and for Bitcoin as a whole. I mean Bitcoin won't be affected directly, but it will be diluted. The incentives don't work with e cash mints. The incentives are similar to those of our current system.
LN is great, but a pain in the ass if you want to be 100% self sovereign. It seems really really hard to scale self sovereignty and also privacy as we would like it to be.
I became a bit disillusioned in the last weeks and months.