Owners manual and sticker on my chain guard specify the slack 1.2" - 1.6".
Also states, Do not ride your motorcycle if the slack
exceeds 60 mm (2.4 in).
The 1.2 - 1.6" spec pretty well translates to 1-3/8" to 1-3/4" when measured on the centerstand.
The "do not ride" guidance means that it could be dangerous over that. The chain could hang and lock the wheel.
3/4 to 1 inch is ludicrous. When I got my "warranty" chain, the Honda dealer set mine up too tight as well. On the way home I could hear it straining any time the suspension compressed on a bump. I pulled over and adjusted it on the side of the road. You can damage the counterstaft bearing in short order with the chain that tight. There is not a single proper amount of slack for a motorcycle chain. It depends on the geometry of the suspension. For our NC's the range given on the machine are fine unless the suspension has been modified.