I have been raiding since SB (and retired this tier), and I do think savage actually exacerbates the scripted part of the DDR quite a lot. In normal modes you have a lot of seemingly random mechanics even though they still follow a script (mechanic A happens, then mechanics B happens, then C, and always in that order, like in savage), because the solutions of said mechanics don't involve a single, unique, unchangeable solution where everybody stands properly in one specific spot else you wipe. In NM players don't have to follow that impetus because while the DDR is scripted at the source, it is a lot less constrained, and therefore scripted, at the resolution end.
If anything, savage isn't necessarily faster than normal modes, especially in DT, or, it really depends, but I wouldn't consider it a defining factor there. If you take a look at the latest parts of say, P4S, P8S, P12S (as opposed to the frantic doorbosses), they're excruciatingly slow in resolving things, because they're more about puzzles and debuffs and it's been like this since forever (Midas/Omega).