Yes, Mars did. If it hadn’t the asteroid belt would have continued there. There is a genuine difference between how the eight major bodies orbiting our sun formed, by accretion of most of the material in their orbit and then ejecting the rest, and the belt objects that coalesced from the remainders.
That’s one way. Another way is to look at the wobbles they cause in their star’s motion…so far I believe most not found by Kepler are still in that category. Which, incidentally, is a technique that counts large objects that have cleared their orbits but not smaller objects that are part of belts. So far extrasolar belts are detected by infrared excess from the dust they create instead, and we are not anywhere near seeing individual objects in them.
I can see why people might think so but it’s a really awkward definition for three reasons:
- Round isn’t defined and is actually kind of difficult to do so…for instance, it’s tough to say is Vesta is round with a dent or not. You basically have to pick a cut-off and unlike orbit-clearing there is no natural gap there.
- In focusing only on the object’s shape and not size or gravitational influence, it’s hard to justify why it wouldn’t include moons.
- Like you said, it includes a lot of objects and doesn’t match up with the traditional use of planet, where for instance asteroids stopped being considered as examples once it became clear there was a whole belt of them.
It’s true that Mars and Jupiter aren’t very similar…but then that’s actually part of the point. There is nothing quite like Jupiter, only a few things kind of like Mars, and a ton of things a lot like Pluto. Because Pluto is part of a belt and Mars and Jupiter aren’t, which is at this point what planet literally means.
And by the way, it’s important to have a distinction somewhere because there are so many non-planet objects that they need numbers to have any chance of keeping track of them, like 1 Ceres and 624 Hector and 99942 Apophis. Planets never have and that’s ok because there are less than a dozen of them…it won’t if you include little things like 136199 Eris and 136472 Makemake and 134340 Pluto.
It’s so deeply frustrating to me that all these years later people still say that’s arbitrary. They put the line in the least arbitrary spot possible, one where there is a genuine change in how the objects in question fit into the solar system.
You know, it’s funny. I was literally just reading about the fish family Cyprinidae and how it was recently split into about a dozen smaller families, because what they had was too large and not actually a helpful framework for organizing the diversity of different fish being classified under that banner. Bunch of rubes, changing taxonomy just because it wasn’t useful.
This is really what it’s come down to, huh? We’re just going outright slander the interests of scientists because we don’t like the taxonomy they use? Because astronomers definitely aren’t interested in the barely-explored category of Kuiper belt objects. After all, it’s not like they’ve been sending robot probes out to any asteroids and comets. 
God, this topic gets stupider and more frustrating every year that passes. I know it’s traditional to assume that scientists must not actually have any idea what they are doing when it interferes with nostalgia, but come on.
I used to love astronomy and was so interested in all of this. I still am on my own. It was wonderful seeing what Pluto was actually like, it will be wonderful learning more about all its kindred, and it will be fascinating to see if Brown’s hypothetical ninth planet can be found. But I hate that every single report on it is an excuse for people to go on about how they don’t understand what Brown and the IAU were thinking as if that’s something wrong with astronomers and not themselves. 
