Not sure I agree with the unlearning part as my players had no issues with BiTD... It's pretty traditional in it's player side mechanics... of course we are speaking to whether the GM has a higher cognitive, mental, etc. workload than the players In BitD (After running it I still believe they do) not whether it's harder than D&D (I don't think either is "harder" in an objective sense but running them requires different skillsets which may be harder or easier for some to leverage.).
My players found the ability to introduce elements into the fictional world to be a pretty significant departure from D&D. And also things like players deciding what Action is relevant, and players deciding how much XP they get.....although these were easier things to grasp.
On the GM side, I don't know if there's more cognitive load for Blades. I think that the system is there to do the heavy lifting so that the GM is free to determine the specifics of the outcome that the dice have called for.
What are these techniques? And would they do that universally for anyone who leveraged them?
I think a big one, for me anyway, is the idea of a Partial Success, or Success with a Complication. Those 4s and 5s in Blades are what drives a lot of the fiction, and I've found I can adapt that to D&D very easily, and suddenly encounters are becoming a little more dynamic because I'm adding complications or setbacks throughout.
"Play to find out" is an ethos that I've found is very helpful for any game I GM, even if it isn't a perfect fit for a specific game, like D&D. I've found that blending that mentality with the kind of prepared elements typically associated with D&D makes my game smoother, and focuses me on what's happening in play and not so much what I had written prior to the start of the session.
Then there are always other specific mechanics that can be swiped from one game. I mentioned earlier in the thread that we've ditched the default 5E initiative process in favor of the one from Modiphius's Star Trek Adventures. I've also instituted an Inspiration Pool where there are extra d20s and any player can use one at any time to gain advantage on a roll, or they can use two to roll over. These alternate elements don't work wonders to speed up play, but they do make things more dynamic and the players are more engaged and aware, which does wind up taking the load off of me.
All this stuff is subjective, of course, and what works for one person may not for another. I'm sure there are plenty of other ideas out there that we could come up with.