The chain was used because it was the best way of keeping a true length that was also easily transportable.
Rope stretches, and as the fibres age, it frays and shreds and fails.
Tapes are only as sound as the material they're made from, which usually stretches, and if coated, differentially depending on temperature.
Someone asked me once why they didn't just use bars of a certain length, like half a yard, joined together into a chain, and having handled 'slave chains', made just so, I can tell you bluntly that they don't pack tidily, they don't flex easily, the bar links judder and clank and wrench and pull and do not stretch out easily either.
A chain made of small links though will drop easily into a bag, will flex and pull straight easily to give a true measurement.
Engineer's chains are made of shorter bar links, but they're a pain to pack and store....bit like folding up modern LED Christmas lights, iimmc ?....and if I recall correctly they're 100feet long.
I believe that chains are still widely used in India for cadastral surveys, but they've gone metric now.
There has to be an online site about all this. Surveyors still use 'chain' measurements for some things, even though Archaeology only uses them for understanding past distance references.
M