It would be interesting to see how well players can accurately judge the strict zone in real time.
I suspect they'd be no better, on average, than the average MLB umpire. Chiefly, because MLB umpires are largely selected for this one specific ability, while players are selected for this plus many other abilities (like reflexes, coordination, strength, etc.) -- heck, there are probably some players like Astudillo or Vlad Guerrero who could be relatively poor at it, but it doesn't really matter given their other abilities and approach. Plus players would seem to have a disadvantage of perspective -- the batter stands off to one side looking away from the plate most of the time, while the pitcher is much farther away from the plate. (The catcher might have the best view, I suppose. I wonder how they'd agree with Statcast? Although they would seem to be an example of the differences of perspective too -- I don't think that catchers generally have a better eye when batting.)
Anyway, it seems to me that players would have their own disagreements with a strict Statcast zone -- and many of these would overlap with the umpire's. For example, let's say there is a ball clipping the edge of the zone, a spot where the umpire generally calls it a strike 75% of the time, and a ball 25% of the time. Even with a 100% accurate robo-ump, calling it a strike 100% of the time, a player still won't be able to detect it as anything that close to 100% a strike, in real time from their vantage point -- they may have the same 75/25 split as the ump. In which case, you may not see any "true performance" difference in that situation under a robo-ump system.
And extending that to something like the umpire's "two strike bias" referenced in the study -- players could have their own similar "two strike bias", because 25% sure may not always be sure enough to take with two strikes.