I don't currently own many guitar with vibrato and the strats I currently have, I have blocked the bridge for personal preference reasons. However, every guitar I own or have owned stays or stayed in tune. Even the ones that I did not block the bridge or Gibsons, which the internet says have an inferior design headstock compared to other guitars like Fender, PRS, Ibanez etc. My secret is that I take care of my nuts. Every guitar I own or have owned, the first thing I do to it is make sure the nut slots are sufficiently wide for the gauge of strings I'm using. Most guitar makers do not spend enough time making sure the action at the nut or making sure the slots are wide enough for the strings the guitars are shipped with. Almost every guitar I've had required a bit of touching up. The only ones I can remember didn't require a touch up were my Gibson Custom, core PRS, a Gibson acoustic (studio), and two Gibson USAs, one of which had titanium nut, so I don't really count that one. Martin, Fender, PRS from CE down, most Gibson USAs, LTDs, Samick Greg Bennett etc. all needed some adjusting at the nut. PRS SE's, for instance, were notorious for poorly slotted nuts (they seem to have gotten better since 2018), hence the popularity of MannMade USA aftermarket bridges and locking tuners or nut replacement. Some of the worse dressed nuts I've ever seen were on PRS SE's. I saw one that you literally had to push the high E string with force inside the slot even using 9s. I saved friends so much money by addressing their SE tuning issues just by just dressing the slots properly. Thus, while I have worked with vibrola guitars before, I don't have a ton of experience with these particularly vibrato systems. However, I'm inclined to agree @fuzbuzz78 here, because, although I have encountered cases where a bridge was the main culprit of tuning instability, I found those to be very rare and more often than not, nut unhealthiness is the main villain of tuning problems.