Noting of course that in the subject line, "waltz time" means 3/4, and standard time is 4/4. The reason other time signatures sound more "interesting", so to speak, is that they aren't as regular. For example, in 5/4, the stressed beats are usually 1 and 3 or 1 and 4, so you get "ONE two THREE four five ONE two THREE four five", or "ONE two three FOUR five ONE two three FOUR five", so it kind of lurches along asymmetrically like a guy with a dead leg.
Similarly, 7/8 becomes ONE two three FOUR five SIX seven (usually counted under your breath as ONE two three ONE two ONE two), so it's like a three-legged zombie. On speed? I dunno, similes can be hard.
3/4 doesn't get subdivided into more than one stress per bar because 3 is an easy number of beats to keep track of, and 4/4 easily gets divided into 2 and 2. 6/8 gets easily divided into groups of 3 so it's kind of like a double-speed waltz, so you get something like a jig/gigue. That's why it seems "natural" to invent a melody that fits into those time signatures, and more "difficult" to come up with one that sounds like it "should" be in 5/4 or 7/4 or 11/4 or whatever (note they are all primes! 9/4 or 9/8 is easy - it's like a cross between 6/8 and 3/4, and obviously 12/8 is super cool).