If there's space for only three non-overlapping bands, there will only be space for only three non-overlapping bands, regardless of how the channels are numbered. A more interesting question is why there are more than three channel numbers; the answer to that comes from the fact that WiFi is the 2.4GHz band is used for many kinds of devices besides WiFi; some of those devices, such as analog audio/video transmitters, may require a "full-time" channel allocation. Such devices are no longer terribly common, but their existence would have influenced the creation of WiFi standards. If a few such devices which each uses 5% of the available bandwidth have four-way channel selector switches, with different devices offering different but overlapping sets of frequencies, it may be that the only combination of available frequencies which would allow everything to work without interference would have something in each of the three "main" WiFi bands, but that a shifted range of frequencies would be available for the WiFi.
That having been said, I think things would have been far less confusing if the channels had been labeled "1-5", "6-10", and "11-15", (along with "2-6", "3-7", etc.)