"What is the effective range of a typical red dot sight"
It is ALL ABOUT your eyes when using a Red Dot. If you can see it, you can shoot it. I am lucky, I am in my late 40's and my eyes are still good so I think a red dot on a AR is the perfect optic for 5.56 rifle.
On our property I shoot two different sized steel targets with my AR's. Small (8in wide X 11in tall, think head shot) and Large (18in wide X 24in tall). The larger target is a full size IPSC so man sized torso.
I can hit the small target standing out to 100 yards consistently. Past that it gets hard to be consistent unless I get support. I can shoot it consistently at 200 with support (prone or using a barrier). In fact this is the target we use with the AR and other rifles out to 200 yards to practice for deer hunting as its basically the size of the vitals box on a deer. We sit up in a deer stand that has a rail for support and hit this target setup at 200 yards. Past that with a red dot and it starts to get hard to see, especially once the white paint gets shot off it and its grey. When its grey it starts to blend into the background.
I can hit the larger target with my AR, standing, out to 200 yards. Past that I use support. My property only allows out to 400 yards without tree's, barn or whatever getting in the way. We easily hit the target at 400 with red dots when shooting supported. I just place the red dot at the top middle of the target and drop of the 5.56 round hits about the middle of the target at 400 yards. I could probably use the same method out to 600?, if I could see the target.
The big thing to remember with a Red dot is that is has NO eye relief. So it is great for fast up close shooting. Any magnified optic is going to have eye relief so it will be slower and not work great at close range. IMHO I would never use a 1x4 or any other magnified optic on a AR for home defense.
The comment about a red dot on a AR being perfect for a battle rifle is exactly how I fee. 0-200 yards head shot, 0-300, 400, 500, 600? with a red dot minute of man.
I have shot soda and silly string cans at 200 yard on top of a 55 gallon drum with my Sport using a Eotech. It took a few shots but when you hit them you knew it, especially the silly string.
You also have to remember that with a typical 55grain 5.56 round is starts to lose its ability to tumble and frag past 200 yards and that is out of a 20inch barrel, from a 16inch its probably past 150 yards. Point being at ranges like 400 yards it is a fast 22 that pokes a 22 hole.
Scopes are becoming popular on AR's, especially the 1x4, 6, 8 because of 3gun games. For that application, shooting static paper/steel targets at various ranges out to some good distance the 1X is great option. I don't agree with that for a home defense AR.
What I do find really odd is when people put a scope on a SBR AR. Scoping a 10.5inch AR does what???? Unless you are using some expensive rounds a bullet coming out of a 10.5 inch barrel won't tumble and frag past 25 yards if at all. Putting a scope on it so you can shoot it long distance from a 10.5 inch barrel???? To each his own.
I have a Eotech 2.0 on my Sport and a Aimpoint Comp M4s on my BCM. Both are great. The Eotech has a smaller 1.0 MOA dot so it is a tad bit more precise over the Aimpoints 2 MOA dot, but it really does not matter for what I am shooting at. I personally think the Aimpoint Comp M4s is currently the finest red dot made. It is a TANK and with a Lithium AA battery the red dot can stay on for 8 years. The only negative of the Comp M4s is price, at over $700.
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