For DQN, the issue is finding the max below for a continuous space.
It is not impossible. We just need some kind of optimization method to solve max Q. But that can be inefficient.
But for RL, I learn never to say never. Algorithms can also change to address what it is originally missing. DDQN is for continuous control. I wrote something on it but have not a chance to review and publish it. So you may have to read the original paper first: