I haven't found any critter issue on the grass. But 3" isn't 4.5"... (not to say I don't let it get that high before mowing, I just know I don't mow often enough!)
It also really hurts the lawn to cut more than a third off at once. You'll find a lawn frequently mowed at 3" needs little in the way of anything, and certainly no poison. The taller grass has a proportionately deeper root system, so more water access. It also shades the ground, which keeps it cooler and helps prevent weed seeds from germinating.
(I assume you know about deep watering - water rarely and for a long time on developed grass)
There's a lot of good stuff out there on this. You'll find its easier, cheaper, and healthier to work with the grass rather than making it a lab experiment.
And I just wouldn't put poison down on something my kids were playing on. They regularly find "oops, we thought it was safe, until everyone who touched it got cancer"
Don't get me wrong, I deal with a lot of poisonous materials. Sometimes you have to use hazardous stuff. But it seems silly to me to use it when you don't have to.
Your lawn is beautiful by the way!