I think the differences in the designs of DSC vs TOS can best be explained by Voyager's "Future's End" episode. In this episode we learn that the computer revolution of the 20th century would not have happened if not for Henry Stalling interfering in the past. So, if we assume that The Cage & TOS happen in a timeline with no meddling by Stalling, and ENT & DSC happen in a timeline in which he did meddle, this can explain why the latter two shows look more advanced and use more advanced technology.![]()
That would make a certain amount of sense (if you need to justify it).
I'd also suggest that the design (especially of starship exteriors) is likely to have been influenced by Lily Sloane and Cochrane's knowledge of the Enterprise-E.