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My example I have in mind, is a charity in the developing world in a really broken, poor country.
The locals don't have the sats to open a lightning channel, and they can't trust the 'custodians' to give them their funds in the region where they live.
And they can't afford the on-chain fees, main-chain, just to accept enough UTXOs to open a lightning channel so they are left with 2 choices.
Either not use Bitcoin because it's not affordable... (provided they can run BTCPay server at all) or...
Run BTCPay server on a website, accept donations via lightning QR code (BTCPay) and have those donations automatically converted to Liquid (Lightning->Liquid).
Once enough Liquid UXTOs build up to a few hundred thousand sats... they're used to open a lightning channel. The liquidity is then managed automatically for them as "receivers" using Liquid
With the ultimate goal of stacking enough sats to create long-term, savings-oriented, fee-efficient Bitcoin UTXOs that they can use for important reasons.
That is the purpose of Liquid - it's not 'to use Liquid' it's just a temporary medium in struggling parts of the world.
You keep talking about non-custodial and self-custody but what you have non-custodially is not Bitcoin.
The fact that you need an essay to explain all of this is telling-- It's too complicated.
I really get where you're coming from, and I have nothing against Liquid per se-- it's a decent way to get some privacy. But teaching someone Liquid before teaching them Bitcoin is very much putting the cart before the horse.
I know you want to give them some sats but Bitcoin is complex enough already. Even if it takes 10 minutes and a dollar to settle, I would much rather send on-chain to a noob. They need to understand the foundations before learning about side chains or even lightning.