If lightning doesn't prove to be the best solution, it won't be because of centralization or privacy concerns. Those are both improving rapidly. It is easier than ever, and getting easier every day, to run your own node, very privately. There will almost certainly be very large nodes, but they still are not at all a point of control or failure.
Discussion
Nonetheless, if lightning doesn’t do the job we hope it will won’t it simply be replaced with an improved L2 as dictated by market forces?
Logically, yes. Or Bitcoin settles into status of exclusively-store-of-value. Or gradually fades into obscurity and relevance only to nerds of obsolete tech, like guys who rebuild old cars or argue with each other over the syntax of dead languages.