ProPhoto doesn't have more colors than sRGB if we are using 24 bits to define the color space. The scale however is quite different. And since ProPhoto RGB has a wider gamut, the spaces (distance) between the 16.7 million colors in a 24 bit definition are wider. Think of sRGB's 16.7 million colors to be 16.7 million dots painted on a half inflated balloon. Think of ProPhoto as having the same number of dots, but this balloon is now twice as large. The distance between each dot is farther apart.
This discussion raises some interesting points. With a bit depth of 8, both sRGB and ProPhotoRGB have 16.7 million encodable "colors". With sRGB all of these colors lie within the gamut of human vision, whereas some of the ProPhotoRGB colors lie beyond the gamut of human vision. Therefore, sRGB has more encodable values within the range of human vision. Since color is a perception, differences in encoded color values that can not be distinguished by humans are not really discrete colors. The standard for expressing the difference in color that can be perceived is Delta E
(ΔE) and the volume of a color space can be expressed in terms of ΔE^3. Bruce Lindbloom lists the volume of various color spaces on his web site under the tag of information about RGB working spaces
sRGB has a volume of 832,870 ΔE^3 whereas ProPhoto has a volume of 2,879,568 ΔE^3, and the number of perceivable colors in both spaces is far less than 16.7 million. ProPhotoRGB has more colors than sRGB, but whether or not one should use ProPhotoRGB depends on what colors are actually recordable in the scene. For most natural scenes, the gamut of ProPhotoRGB is unnecessarily large. Lindbloom has devised a BetaRGB that covers real world scenes and Gernot Hoffmann
(warning: large PDF) has a plot of real world surface colors that are important to reproduce in photographic images. The area enclosed by this plot is larger than aRGB and smaller then ProPhotoRGB.
Choosing a "just right" space for each image is impractical, and IMHO 16 bit ProPhotoRGB is the best choice for general use, at least for images rendered with ACR. If ACR could render into an arbitrary color space, BetaRGB would be a reasonable choice.