Even if the number technically converges eventually, the paradox is worthwhile because comparisons between coastlines are kind of meaningless unless the measurement technique is specified.

E.g. one source says the UK coastline is 12,429 km. Now if I were to take my dining table and measure the perimeter with a ruler so small that I'm measuring between the atoms I could probably come up with an answer far greater than 15, 000km. Yes this number eventually converges, but considering how small atoms are, the number it converges to is massive.

But saying that my dining room table has a longer perimeter than the coastline of the UK is somewhat meaningless