Thats not actually how vision in sports work. If you look at research on "quiet eye" an athletes performance absolutely improves when they are able to focus for longer on the ball. If the ball disappears, then performance decreases as focused gaze is broken.
This explains why there's been an arms race of shady serves and trying to hide the ball with your head for as long as possible amongst pro players. The science says that it messes with your ability to judge. If it didn't confer a benefit as you say, then players wouldn't be doing it so much.
Even if players sometimes can judge serves properly with the ball hidden, that doesn't mean the receiver is not at an disadvantage. Your brain having to compute the ball path and register the reappearance of the ball behind some dude's head carries a mental load which could be applied for other focus tasks. Eye tracking is king, and can't be substituted with mental maps. We all know this when we dump a shot into the net when we fail to look the ball into our racket.
The weight of scientific evidence goes against the framework you provided. But with statistics moving forward we can probably get hard numbers to confirm one side or the other. If you're right, then known ball hiders should have the same amount of service win percentage in TTR events as they did last year with poor enforcement. I'd bet on that figure being lower.
While I do accept that it can have some effect, the "quiet eye" phenomenon isn't exactly the case here though and ties in with another point that I've made in the past.
For one, the "quiet eye" applies to hand-eye coordination, which would apply to the server at the point of contact, and the receiver only a bit later when he's about to making contact. The timing is close enough though that there can be some minor effects, specifically affecting your ability to judge the service based on the ball itself. However, this leads to the second point.
The second point is that services are primarily judged based on the server's racket (direction of brush, contact point, contact speed, etc.) and less based on the ball. I've made the point before that one of the reasons hook serves are more difficult to read is because the racket is oftentimes behind the body until right before contact. Top players manage to use the same trick to hide their pendulum service swings as well by keeping their body bent and arm raised (e.g. WCQ and to a lesser extent ML). This IMO is where the "quiet eye" phenomenon really matters.
@Tony's Table Tennis I wonder if the pros you're referring to is actually more affected by the hidden racket path rather than the hidden ball path when they're playing against players who would obscure the ball path. After all, the racket movement is more important for judging a service and it has far more variability than the ball path. What players do to obscure the ball path, e.g. turning their body and bending down with their head close to net height can also obscure the racket for longer than the ball.
