I mean, I get what you're saying, but in the grand scheme of "what effects do zone starts have?", I'm not saying the effect is zero but what I will say it's that there's about 50 other things going on that effect overall production much more, to the point where zone starts are irrelevant. It's like looking at a fatal car accident and suggesting that the scent of the air fresher matters when the road, driver skill, speed, type of vehicle, etc have a much bigger impact.
The example with Acciari doesn't really help. Again, I believe this is a narrative where you are skipping over several much more significant factors to illustrate a point. You could run a simple regression analysis overall all available metrics and the Rsq value of zone starts would be minuscule. This might be a good example of "correlation does not equal causation."
Acciari was brought in to anchor a defensive-oriented 4th line. With that, he's getting 4th line players with 4th line minutes. Put that on top of Sullivan's system, where historically, we've watched productive players lose production, worse linemates, and a different role with likely less ice time (didn't look); it's not hard to see why there is a dip in production. Worse for the case is the fact that merely stating "14% ozone starts make him bad" ignores how many times the players shift starts on the ice, special teams (Acciari was a pk'er for us), and even neutral zone starts.
If you want Acciari to score more, there are more impactful things you do outside of zone starts: put him in the top 6. This will come with more offensive zone starts but more importantly, it gives Acciari two high skilled player, for example Crosby and Rust or Malkin and Rakell/Bunting. Perhaps most importantly, it increases his ice time. More ice time with better linemates >>>> "zone starts" when you see a boost in production there. You can also put him on the PP. Again, that will count as a "zone start" but the fact that he's playing 5 on 4 and it likely with a group consisting of Sid, Geno, Letang, and Karlsson, yeah we would most likely see a boost in stats but it be beyond disingenuous to suggest that it's the zone start in that case and NOT the man advantage and not the significant increase in linemate abilities.
I'm sorry, man. There's just so little evidence that zone starts have any significant effect on a player's production. There's just SO many other things that effect it before zone that it's impossible to say whether or not it has any effect.
Career and Game by Game Stats and Shot Maps For Each NHL Player
moneypuck.com
Here's his moneypuck chart. 53.7% start on the fly. Overall, 31.1% start in the defensive zone. 5v5, it's 26.3%. So a quarter of the time, he starts in the dzone, 56% on the fly, the rest in the neutral or ozone. And you're suggesting THIS is why he sucks? In 2019, 5v5 he potted 25pts in 65gp with 23.3% dzone starts. You're telling me that Sullivan insisting he start in the dzone a mere 3% more is the sole difference in him dropping down to 7 points in 55GP? No. Not buying that one bit. Maybe Acciari sucks?
You can call it "usage," and that would be fair. He's been a primarily defensive use player. He's been given sucky, defensive-orientated linemates and Sullivan's system is stale and sucky. That would all be fair. Zone starts? Lol, no.