Why are there are so many words for "zero"?
Solution 1:
It's not that there are so many words for the digit or number zero, but that there are so many words for 'nothing' which are then associated with the mathematical number.
'Why' is a question we all want to know the answer to, but is often difficult with words. The usual way to deal with it is by turning the question away from causes into description; 'here is the data, it just is'.
Zero, and other numbers, are usually strange grammatically. They're usually adjectives ('five sheep'), and yet also sort of nouns ('Sheep? I have five.' (notice that 'red' or 'hungry' don't fit there). The small numbers all have multiple versions too: one - single, ace, singleton, nonce, loner, two - pair, deuce, double. Zero might be considered special because it really wasn't a 'thing', as a mathematical number, until, let's just pick one to set it, 458 AD in India. But that's a bit of misdirection because 'nothingness', or 'nothing' or 'nought', and separately, 'zero' and 'cypher' have much longer etymological histories than just for a little symbol used in arithmetic.
Given only the recent introduction of that little symbol may be motivation for wondering why it has such a rich vocabulary. But I think that is where the answer lies, in that there is ample historical use of the concept of nothingness, without any kind of specific mathematical notation, that one could expect lots of vocabulary items for 'nothing'.
After all, there are a lot of words for not nothing: much, many, several, a lot, a few, boatloads, numerous, myriad, etc, etc, etc. without having to posit some arcane numerical system (arcane because it was the province, in any society, of the very small set of bean counters; before modern education, literacy was rare, and numeracy even moreso).
The explanation of why there are so many words for 'zero' is really that there are so many words for 'nothing'.