For that to be true there would be plenty of places where it's falling. Are there?

there absolutely are, a google away https://tidesandcurrents.noaa.gov/sltrends/

But they are generally rising, just not more than compared with pre-industrial era.

I mean, "plenty" isn't really true based on that link.

A best you could say "a few, in areas that are losing glaciers, which is expected due to basic physics"

That map clearly shows that only a few locations are experiencing a fall, so neither "plenty" nor summing to zero as claimed. But I'm interested to learn more about the evidence that the pre-industrial trend was the same, since my inexpert googling suggests otherwise, eg "Exceptionally stable preindustrial sea level inferred from the western Mediterranean Sea"

https://www.science.org/doi/10.1126/sciadv.abm6185

It's risen ~97mm since 1993. The rate of increase in that rise has been increasing steadily since ~1993. The consistency of our data has also been much better since then (previously it was only the highly noisy coastal tide gauge data).

Fun fact: the slowest its been in the last century was when we did a crap-ton of dam projects in the 50s-70s, still rose, but very little.

Last I looked at the data, sea levels in Key West had risen by around one foot in the last hundred years.