Good question. The initial idea for the badges was simply to give them based on number of questions asked. For most sites, that would probably have been a fine choice. But a few sites (notably our flagship, Stack Overflow) get more questions than they can reasonably handle each day. The "on separate days" requirement exists to encourage pacing oneself and make questions count. (Most of the other requirements are intended to encourage more interesting, not just more, questions.)
On smaller sites, it can actually be useful to spread questions out a bit. I conducted a contest on Parenting and found that it's harder to care about answers if you are trying generate questions for reasons other than curiousity. My experience on other sites is the same: if I try too hard to ask questions, the answers don't tend to matter as much to me. Also, it can be annoying to see the front page cluttered with the questions of just one person.
You should feel lucky I didn't get my first idea to solve the problem: "on separate weeks". The trouble with that pace is that people would need to wait up to 7 days to ask their next question if they didn't want to "waste" it. I called that behavior "just-too-late asking". A day didn't seem like too much time to wait in contrast. ;-)
And, of course, there's no reason to not ask a second question on a second day, if you don't care about the badges.