Hmm, try the other way around. The slower your transition times, the smoother the in-place transition, producing ghosting that actually happens on the screen, rather than the "in the viewer's brain" one, that I mentioned; They are not the cause of judder - that is having full persistence, although they are the cause of aforementioned temporal smear, which, as you suggested, we do not want to have to watch.
That the strobing masks these transitions, is more a happy side effect than anything else, certainly not the fundamental reason it is implemented, which is, again, to deal with the persistence issue, and its resulting psychovisual "judder" effect.
These slow transitions are such by design, basically implemented by engineers stuck in an analogue mindset -- the actual transmissive liquid crystal materials can transition much, much, faster, when the driving circuitry is not deliberately made with latency incorporated.
So the strobing thing is independent of the display technology -- the very main reason we got OLEDs in the Vive and Rift in the first place, is that their rapid transitioning made strobing possible - without needing to rewire any backlight, much less any active matrix drivers.
Today we have LCD panels where we do have better control over the LED backlight (rather than older and less responsive CCFL), even if the active matrix remains sluggish and analogue in kind, making them a viable cheap alternative, since we can strobe them, just like we do already with the OLEDs, and consequently also have global refresh (as opposed to rolling shutter, with a full frame that is snapshot in time, and can not adjust on-the-fly for your head movements, while the refresh scans out), just like with them.
Frankly, the thing with TV advertising spouting utter nonsense is beside the point; That the marketers do is an absolute given - they are going to do it at any given chance - it's in their DNA. -If they say that a blank period between frames obviously counts as a proper frame, that is not the same as the engineers having had that exact thought in mind, back when they implemented it.
Transition, you should see not as a black band, but as a crossfading gradient (thankfully, I suppose the strobing got rid of that).
If I have a 60HZ rolling shutter monitor with less than full persistence, and a camera with the same, and end up so unfortunately synced that the camera leads the monitor, I will get just a black screen in my footage - if the monitor is 120Hz and still low persistence, I will get the effect of the monitor raster scanning twice in the time I'm capturing (scanning down) one frame; Persistence matters, and having a display that is speedier than one's camera does not necessarily mean I'll get a flawless picture.
If we want more than 60 real frames, we're going to need higher than 60fps content, or at least interpolated frames (...which make up a whole pallet of cans of worms in themselves - "soap opera effect" and all that).
I take it, then, that you only have incadescent lighting in your home, and in fact prefer the slow LCDs, which do not need high refresh rates to hide their strobing. Flourescent lights have always flickered naked-eye noticeably at mains frequency (although today HF electronic ballasts are replacing traditional electromagnetic ones), and LEDs are PWM:ed at a what is usually a significantly higher than mains frequency, but their phosphors has much less sustain, making their amplitude shifts towards infinity stronger.
Heck, traditional film cinema projectors multiplies their shutters: Every frame is shown three times, in order to increase the strobing from 24 (feed the next frame into position during the blackout) to 72 Hz. (...and this is something cinematographers have discovered they have to back away from now, as they began to shoot higher framerate movies, since the repeated showing of the same frame caused the persistence judder we are becoming familiar with, especially given the 48 or more frames per second footage has very little motion blur, compared to the blur from long exposure times, that was necessary to make 24fps palatable motion-wise)
It's going to take significantly higher frame rates than we have today, though. If not through sheer brute force, it could happen through on-HMD frame synthetisation, or by at long last throwing out the legacy "frame" paradigm, and updating individual pixels, on the screen, the very moment they finish rendering, which could be viable, once we have raytracing that is fast enough.
If you have data from properly conducted measuring, I'd certainly love to see it.