The fusion doesn't negate anything. It prevents effects activating. None of the fusion's effects activate. So they'll lock eachother down if they're both Dragon-Type due to something like DNA Surgery.
Wrong. Dragon destroyer does have it's activated effect.
In short, the first player who achieve board control I.e. Dragon destroyer + dna surgery will achieve lockdown. Second player to summon Dragon destroyer will have his monster turn to Dragon type and unable to activate it's effect.
You're acrtually incorrect here, Destruction Swordsman's effect is a continuous one, not an activation effect. Because of these each player would lock each other out in a mirror match unless DNA surgery can be removed from the field
You just have to play smart. If 1 DNA is active, both players can use each other monsters as fusion material. And if both have BBDDS out it will be a lockdown. But you can still change type with your own DNA, change to something else other than dragon. Your opponent can't use your monsters to fusion summon and there won't be a lockdown