I believe your analogy is correct - people are naive now just as they were in 2011-12ish, but there is one huge difference (independent of all the hard work that might or might not get done to make LN privacy better):

LN transactions are not publically broadcast to (and then saved by) the entire world.

And even though actors will (and probably already are) trying to real time monitor and log traffic, it is very hard, or impossible, for them to do it, and it gets harder all the time.

Notice how this differs from on-chain - precisely because everyone has to be in lock step, you only need one monitoring node; on L2 the whole point is that everyone is not sharing state, so you realistically can never know what you don't know.