Asking the right questions, as usual :) If Jimmy cannot use onchain bitcoin *at all*, then Jimmy can never be a first-class user of Lightning (i.e. not having to trust anyone else). That's trivial logically speaking, right. Which just illustrates that Lightning has never been a *full* solution to bitcoin scaling, only ever a partial one; but that was clear from day one, from the paper itself.

Here I define "full" as "available for billions, not millions or less people".

I think it very doubtful we will get such a full solution, ever, but I'm not sure. I tend to believe ZKPs are the path via which we will get there, although I wouldn't be amazed if just a few extra bits of expressivity in Script could achieve big steps forward on their own. But only in ZKPs (and probably further, *recursive* ZKPs) will we get the necessary scaling factors of multiple orders of magnitude of compression. Even if we do, the glaring issue of needing fully participating nodes for absolute final settlement might be insurmountable. So, ultimate final settlement for billions seems like it won't happen in this paradigm, but that's probably OK. 

 For anyone who cares, I'm more talking about succinct noninteractive arguments of knowledge (SNARKs for short), than ZKPs or ZKSNARKs, but we tend to use ZKPs as a shorthand.