You're entirely wrong. The solution to that is not to be an idiot and put champions off duty while your rookies are off duty. The wiki is pretty bad on combat in general, in fact. It even lists swords and axes as being equal in combat!
Wrestling causes frequent injuries, especially if dwarves are not trained in armor use. They break bones, crush windpipes, crack spines (this last is extremely common and ruins all subsequent sparring). However, if you give them crappy weapons and decent armor, it's almost literally impossible for dwarves of the same experience and attribute levels to hurt each other (besides gray wounds). The point is not that they dodge the weapons, because even a champion will sometimes be hit. The point is that they don't get hurt when they DO get hit.
The second excellent reason for giving dwarves weapon training first (and only if you have wooden/silver weapons, or at most no-quality copper) is that they are more effective when using weapons against crowds and when outnumbered, and they can still do real damage to creatures larger than themselves when using weapons. If you look up Toady's comments on combat, you'll notice that size is the most important element of wrestling combat.
The third is that wrestling causes armor training to lag behind permanently. Also, weapons skills give more attribute boni per level gain. So even though wrestling trains faster, it's less useful for building soldiers. If you want a balanced end product, wrestling is the last thing you train (it will almost be legendary by the time you max weapons anyway).
The biggest part of sparring is not to put dwarves with very different attribute levels or experience levels off duty at the same time.
Another important consideration is effectiveness in battle: a weapons soldier with +5 training in weapons will slaughter even a full ambush squad of goblins (almost always if using swords; they're overpowered at that level, but any weapon will do), while a wrestler will have to fight each goblin one at a time (causing exhaustion, allowing him to be mobbed, etc.).
And it is 10x as important if fighting a larger opponent (such as with orc mod), as size is the most important factor of wrestling combat.
Finally, giving a weapon to someone with a base of 0 (out of the possible 15) is a good way to make a soldier useless. And if you really want someone to survive melee with more than one opponent, they need a weapon. So, you should train weapons to a minimum of 5 or so before going wrestling, then max wrestling, if you want the most effective early soldier. You can send them into combat and expect excellent results with around level 5 weapons training. If you want to max his/her capability in the long run, you'll max weapons before going for wrestling. There won't be much training left to hit legendary wrestling then anyway. And unlike your soldiers that max wrestling first then weapons, they'll have legendary + armor and shield proficiency.