As I understand it, the first phrase is common. I'm afraid, I don't understand why is necessary the second "for" here (in bold). I think "to" is necessary here because "good men" isn't the subject, but the object.
The second phrase is mine. Does that sound good? Do you use only the first version as a standard phrase? Maybe you usually shorten this phrase like me. I think the second phrase has the same meaning as the original.
The only thing necessary for the triumph of evil is for good men to do nothing.
For the triumph of evil needs good people to do nothing.
Best Answer
It is not a “standard phrase” but a quotation from Edmund Burke. (I have not read enough Burke to identify the exact source from memory.) We do not misquote quotations because we do not like their style. Burke’s is the high literary style of the eighteenth century.
Your rewriting is not grammatical. Here is a grammatical version:
However, that rendering does not express the original meaning.
Your analysis of the grammar of the original is wrong. “For good men to do nothing” is the complement to “necessary.” The grammar is hard to decipher because Burke plays with word order, ellipsis, and the wide field of usage of “for” to render an implausibly optimistic thought memorable and plausible. Here is a slightly revised version that makes the grammar and logic easier to analyze.