grammaticality - Why "hundreds of s" instead of "hundreds of "?

In the expression hundreds of <noun>(s), I would think that hundreds is what's being modified because of is usually right-branching:

hundreds<-{of <noun>(s)}

(This is in contrast to X hundred <noun>s, in which X hundred is clearly the modifier, and hence the plural.)

If so, I can't see any reason (apart from overwhelming usage, of course!) why <noun> must be plural. To me, the idea expressed seems to be a multiplication of some sort:

X00 * abstract instance of <noun>

(This would then be similar to the formal "There are two kinds of person.")

Is the singular archaic, and did we somewhere along the way begin thinking more along the lines of {hundreds of}-><noun>s than hundreds<-{of <noun>}, or am I completely off?

Evidence from Google Books:

I have asked many hundreds of person of all classes respecting their own places of residence. (1843)

... there was every reason to suppose that an epidemic would be certain to lay claim to hundreds of victim. (1869)

The officers of Police could point to hundreds of person who lived solely by picking pockets and other selonious acts ... (1792)

I have traveled hundreds of mile by rail, buggy, lumber wagon, and on foot. (1889)

For hundreds of year it was the coronation site and burial ground of Polish monarchs, saints, and national heroes. (2010)