I believe this is related to one of the meanings of も.
も - prt. A marker which indicates emphasis.
It's used in sentences like:
私は漢字を一つも知らない。
I don't even know 1 kanji.
This can be used the same way with 何:
何も知らない、ジョン・スノウ。
(lit.) You don't even know [one] thing, Jon Snow.
You don't know anything, Jon Snow.
In this sense it doesn't quite make it a universal word.
It just happens that "even one thing" coincides with the more natural translation "anything".
To address the use of よりも, the も is the same emphasis marker. When combined with より it emphasizes the speaker's opinion that there really is nothing better than Okonomiyaki.