Yes, Queens are born through chestbursters, but if there is no Queen or eggs around, what are the drones supposed to do to continue the reproduction?
1. As ALIEN DC suggested, egg-morphing can occur. This would make sense for a survival tactic of the Alien warrior, but the idea of a Queen being the only provider of eggs/facehuggers makes much more sense.
2. The Alien warrior somehow impregnates hosts with Alien semen (through it's tail?)
3. Alien warriors can rapidly change their sex/genetics and molt into Queens as a last resort
Again, I would support the egg-morphing method much more, if the idea of a Queen was never brought into the cycle. Sure, it's possible the Aliens could go this route, when there is no Queen around, but for the host to grow into an egg, thus growing a facehugger...uncharacterstic of the Alien, IMO.
However, the egg-morphing has been established on film, so it would be kind of neat to have future films explore this more, but the inclusion of the Queen is holding this back. If the Queen was not introduced in Aliens and ALIEN DC was released back then, I bet the egg-morphing would still be used now, unless some one (other than Cameron) thought up the Queen or another explaination for the eggs.