Why is it meaningless?
From roughly the 1960s through the end of the 1990s, the number meant printed gate lengths or half-pitch (which were identical).
At some point, companies started using "equivalences" which became increasingly detached from reality. If my 50nm node had better performance than your 30nm node because I have FinFETs or SOI or whatever, shouldn't I call mine 30nm? But at that point, if you have something less than 30nm somewhere in your process, shouldn't you call it 20nm? And so the numbers detached from reality.
So now when you see a 1.6nm process, it's think "1.6nm class", rather than that corresponding to any specific feature size, and furthermore, understand that companies invent class number exaggerations differently. For example, an Intel 10nm roughly corresponds to Samsung / TSMC 7nm (and all would probably be around 15-30nm before equivalences).
That should give you enough for a web search if you want all the dirty details.
Chip frequencies stagnated (end of Dennard scaling if I remember correctly) giving the impression that single threaded performance had stagnated, but since then chip makers have used increasing data and instruction parallelism to squeeze even more apparent single threaded performance out of chips. A 3ghz chip today is usually way faster on average code than a 3ghz chip 15 years ago. They also started expanding into multiple cores and adding more cache of course.
For fab processes we should just switch to transistor density. That still wouldn't capture everything (e.g. power efficiency) but would be a lot better than not-actually-nanometers.
For performance we really don't have a good single metric anymore since all these performance hacks mean different levels of gain on different code.
Indeed
May I propose transistor density divided by the (ergodic) average transistor switching power?
The marketing departments of silicon companies are saving that as their ultimate weapon.
Chip frequencies didn't detach from the reality. However, as you point out, the performance improved regardless because frequency wasn't the only thing that could be improved.
Another poster summarized what happened with transistor 'density'. New techniques were invented that 'effectively' improved performance, and the industry apparently wanted to continue to use this one number as the basic benchmark.
Not really the same thing, though. If I buy a chip that's advertised as 3.4GHz, it'll run at 3.4GHz. Maybe not all the time, but it'll achieve that speed. If I buy a chip advertised as being produced with a 3nm process, there's nothing even resembling 3nm on there.
N1.6 is much better for naming node processes. Or even TSMC16.
They could invent codenames, or start using a better (physical) metric, if this one is no longer relevant.