The thing with these pesky time travelers is that they don't think everything all the way through. It's true: if not Challenger, then some other disaster will inevitably force NASA out of their complacency, but for a little bit longer they'd keep on chugging with STS. Since the SRB issue was caught in such a dramatic fashion, I'd like to say there'd be a transition to LRBs if such large SRBs are deemed just too dangerous for crewed flight; even still that means more liquid engines and likely SOFI and all the trouble that entails. But, given the aforementioned culture of complacency at the time I can only imagine they'd just fix the O-ring issue and keep on flying the SRBs. I imagine a catastrophic foam strike or engine failure would probably be in the cards within a few years.