Brendon, the ideal height is determined by 1: how frequently you want to mow and 2: how hot and or dry the weather is.
You mention you are cutting to a 3.5 inch height, this is spot on for almost all grasses to thrive and keep weed intrusion to a minimum.
I consider 3" a tad short for my purposes and 4" a tad long for my purposes. We cut grass for maximum
water retention and weed control.
Short grass, in my opinion is for golf courses and soccer pitches. BTW golf "fairway" height 1/2 to 3/4", golf "rough" first cut is 1", second cut is 1.5", third cut is 2", then it is usually left at 4"+, soccer pitch height 3/4" . American Foot Ball grass fields are usually also 3/4"
For the best cut, carpet look you want to double cut the grass, this means you cut the entire lawn in one direction then go back over the whole lawn at a 90 degree angle to the first cuts direction. When viewed from a high point a proper double cut looks like a checker board pattern.