I suspect d'autant in particular is a locution and not internally analyzed, but it probably originated from a rule that still sometimes rears its head.
That rule is to insert de before qualifying the degree or number of something. One word in which this has become lexicalized is davantage, derived from avantage and also not internally analyzed:
J'en aimerais davantage. I'd like some more.
You can also see this rule in active use when stating the numeric value of a noun:
L'augmentation est de 150 %. The increase is 150%.
But compare: It's an increase of 150%.
I suppose this rule is an extension of using de to link a qualifier to its noun, as in la Fête des mères, understanding the number or degree to be a quality.