If I want to use an adverb to say, for example:
I'm not sure you could do it. I can say that
percentagely / in percentagethere are few hopes.
Is there a specific reason there is no such word in contemporary English?
There is no such word because there is that linguistic phenomenon called "blocking".
We already have percentagewise, so its existence blocks percentagely from getting any traction, or indeed from being created in the first place.
This is actually the same mechanism that ensures we still have children and not childs, or say unequal but inequality.
Percentagely, childs, unequality are only likely to get any traction at all in a meaning (register, dialect...) different from that of percentagewise, children, inequality.
Basically whenever there are two (or more) different morphological paths we can take, each of them leads to a different meaning. If we have but one meaning to cover, then whatever path we've taken, it won't let us go back and pick one of the others to arrive at just the same destination. This is a basic linguistic mechanism, not limited to English.
I think you are looking for "percentually". It may be less frequently used, but it does exist and its more difficult (= more Latin) formation is what prevents it from being widely utilized (or known).