If color is the "new italic", or the "new bold", then it will be up to the user to decide when letters change color, just as it is up to the user to decide what words are to be set in bold or set in italic. And word processors already let people change the color of text.
Using color as an element of a typeface, so that one takes Bifur and replaces the areas made gray by being striped by color areas, and similar things, is an entirely legitimate action as well, even if doing so now means that the typeface can't be changed in color and still work properly.
The problem isn't that making color an element of the typeform, or using it for emphasis, is not legitimate. The problem is that it is being oversold. (That a new idea has to be hyped a bit to get people to pay attention, though, is another issue - one I am not prepared to address.)
It certainly is true that computers with color displays make it easy to use any combination of colors one likes - recently, I was doing some reading, and I was reminded of the history of artist's pigments. Finding pigments, in the various portions of the range of possible hues, that were resistant to fading under exposure to light, and that were nontoxic, was often very difficult.
And it is because color wasn't easy to use that it didn't become a routine element of typography. The natural world is a colorful place, books and magazines that are printed by a four-color process, so they can have illustrations and photographs in color are appreciated - so the idea that color should become natural and integral to the text between those illustrations as well... perhaps ought not to be rejected out of hand.
But just because people enjoy color, of course, is not a reason to employ color at the expense of readability or legibility. The temptation to mix twenty different colors like twenty different typefaces on one page could have similarly bad results. (But hue values, like grey scale values, are part of a continuum, so disaster is not quite as inevitable in the case of colors.)
The ancient Egyptians, though, used red ink for emphasis. So some limited use of color does have a long precedent.
This discussion has reminded me of an important difference between the kind of font one would order from ATF or Kelsey and a TrueType font file. If one wanted to typeset an entire book, a single 20-a font wouldn't have enough letters in it to do the job, one would have to buy a bigger one.
So a .TTF file isn't a finite collection of letters that can be re-used after one finishes with a given document, it's an endless supply of as many letters as you want.
So maybe we should be calling them TrueType matrix-case files?
Of course, the precedent was already set in the phototypesetting era; the negatives with letter shapes on them were called fonts... I think, but I could be wrong.
And, of course, type designers can certainly call their businesses type design studios instead of typefoundries; that term existed in the metal era.
Caledonia is a very popular typeface; one very tiny footnote to the career of W. A. Dwiggins that few people know is this: the symbols "dek" and "el", used for a while by the Duodecimal Society of America (now the Dozenal Society of America), and which received sufficient public notice that they appeared in a "new math" textbook I used in junior high, were designed by W. A. Dwiggins.
Having owned a manual typewriter which had a cloth ribbon that was red across half its width, so that one could print words in red for emphasis, the idea of color being "the new italic" is not completely bizarre to me.
Since display faces like Bifur served a purpose, defining a typeface where parts of the letters are different in color can't be dismissed out of hand as illegitimate or not properly part of typography. Also, one can find in old specimen books examples of an outline face paired with a face for its interior for two-color printing; similar things were also done for monogram blocks.
Having said that, however, I do share the skepticism of others as to whether this will ever become a big thing.
Now, though, what may become something to be encountered in the future is typefaces where parts of the letterform are defined to be in "color 1", "color 2", and so on, so that just as existing word processing software can choose to print black-and-white letters in red, blue, or any color one wishes, multi-color fonts would allow the individual colors to be altered from their defaults.
Once that happens, then a multi-color typeface could be adapted to the purposes of designers making use of it, and then I could imagine such typefaces becoming a standard part of typography - even if still a minor one.
...and so I'm in agreement with what I see Nina Stössinger posted above.
One other thing: this reminded me of a sequence in an episode of Star Trek: The Next Generation, where a computer screen shows text in an alien language the glyphs of which are animated images of spheres with colored patterns, rotating in different directions.
Given that 18 units per em was good enough for Monotype, on the one hand no doubt 1000 units per em is enough, but on the other hand, a number of units that is a multiple of 18 would provide compatibility.