Well, then I don't understnd your argument for you implying that Q should show up in DSC because of the spore drive.
They didn't back themselves into a corner. Even before the show aired, they showrunners warned us that there would be something that seems to go against canon, but that all will be explained as the story progressed.
I could be wrong, but now after seeing the first several episodes, I assume that the "something that seems to go against canon" is the spore drive. If that is the case, then from what they said back before the show premiered about non-canonical items being explained, I bet they had a pre-arranged storyline that will explain why the spore drive is not a thing in TOS, TNG, etc.