A red dot sight can easily go to the $1,000 range if you're looking at quality, with many filling the $400 to $600 range. I have a Burris FastFire III with a 3MOA red dot. One time I hit a squirrel and dropped it right on the spot from 35 yards using that on a PCP carbine with an LW barrel - an inherently accurate .22" airgun. What I saw through the Burris was a red circle with rear legs and a tail at the moment I pressed the trigger. It was a lucky hit, straight through the heart. I only used it on game that one time. And shouldn't have taken that stupid shot. At 35 yards, a 3MOA dot is just too much bigger than the target zone.
So I use a scope for squirrels - a Burris 2-7x - so that I can place the pellet inside a spot smaller than a dime between the eye and the ear hole. Makes for a clean drop every time. No point gambling with inaccurate optics when taking a life, even if it's a fuzzy-tailed rat. And most of my shots on squirrels are inside 20 yards. If I'm going to have a kill zone that small and nail it every time, as I have for the last several years and for most of the 5 years before that for my now 397 grey squirrels, I want to see exactly where it's going to hit, not just 'aim for the head.' Too easy to injure an animal that way.
So for my 9mm carbine, a 2-10x FFP suits me just fine. I shoot to 100 yards now and again, and it lets me see the holes as they appear. That's satisfying. Lets me make an adjustment to the scope if necessary, or tells me what I already knew about any defect in my timing or steadiness. I don't see any issue with using a scope if that's what you want to use. Anyone telling you it's wrong to use a scope on a 9mm carbine is probably hung up on it being 'unmanly' or some such nonsense. Such people can rarely print a 10 shot group under 6" at 100 yards, with any rifle. They're insecure, and brag about it.