Since we can probably agree that you're not indexing distances or other units of measurement (you can make a piece of string of length sprt(2) centimeters or other irrational lengths!), let's skip the terminology argument. That wasn't my point.
Is skipping the 13th floor a US thing? I don't recall ever seeing it in the UK or Germany.
Counting is indexing!
What is it that you do when you count items in a set? You put them into correspondence with the natural numbers, indicating each one as 1, 2, 3, ... The last integer is the count.
Yes, it is related to the "is the first floor ground, or the one above it"; and it's clear that some programming languages take their cue from stairs and elevators.
Nobody ever has to calculate "what is the floor twice as high as this one?" Moreover, people are unfazed by 13 missing.
(I haven't seen a language that omits 13 from indexing, fortunately.)