That became the standard in order to make it easier to back up your saves (remember, this is the pre-cloud era that we're talking about) when transferring files to a new computer, upgrading to a new version of windows, or reparing a damaged installation (assuming that the entire hard drive hadn't failed yet). Microsoft wanted that as a standard because people were sticking with their old Windows (due to the hassle involved when every game has a different way of making save files in the game's folder), which not only cost Microsoft the money from selling those new versions, but saddled them with a somewhat undeserved reputation as an unstable malware magnet (Microsoft's reputation as being unstable and easy to attack comes as much from the ubiquity of the platform (thus inviting far more attacks then competitors) and the fact that there's so many older versions of Windows out there that it would cost too much to actively support). Game developers wanted the change because too many people were reluctant to upgrade their hardware (which often required a wipe in those days due to the old drivers conflicting), which meant that they weren't able to buy the latest, most demanding offerings. Gamers, mostly, supported the change because it made them less likely to lose saves to hard drive failure, which was much more common then then it is now (due mostly to dirty power, not shoddy design. The increasing ubiquity of UPS devices has greatly reduced this problem.)
At the time, it made a great deal of sense, and was quite popular. Granted, it would have been better to add an extra folder to keep things seperate (putting all the game saves and app data there), but that's an understandable oversight.