"And, as you adjust the brightness of your dot (especially for a bright day), its "visible size" changes - which will move the POI if you sighted in (using the top of the dot) at different brightness."
I have never done any tests with this, but I don't believe this is true. The dot is 4 MOA. It doesn't say 4 MOA with one brightness setting and something else at a different brightness setting.
"the red dot appears kind of "fuzzy" in many light conditions - not like a clearly visible top of a front sight. "
This is something I have experimented with. If you have the brightness setting up too high for the ambient light, the dot will change from round to a blurred image. All that is required is to use a brightness setting that gives you a nice clean, easy to see sight picture and no more. As I mentioned before, this isn't all just theory and speculation. I have done this more than once and it proved entirely satisfactory. Another point about the brightness setting which ties into both points. My Aimpoint has, I think, 10 brightness settings (I am not sure). Even through it has 10 settings (or whatever), I only use three. When I am shooting all day from early moring to complete darkness I use alll three settings. If I go out for a couple hours the sight never leaves a single setting. For example, I normally shoot in bright sunlight at the setting of 8. This gives me a nice clean dot in the bright sunlight we have here in the desert. If I am shooting very early in the morning I might dial the brightness down one click and then turn it back to eight when the sun gets fully up. The only other setting I have ever used is "three" which I use in complete darkness. So, 99 % of my shooting is done on the same brightness setting. Now if this is an issue at all (which I don't think it is) it is only an issue when making long range precision shots, which also are a very small percentage of the shooting I do with the dot optic. Again, this whole nice clean dot thing only comes into play if you are taking a long shot at a very precise target; if you carried the rifle with the dot set on 8, this would suffice for the vast majority of your shots. If you needed to make a long range shot you probably have time to make sure everything is perfect and you might want to play with the brightness setting, however this wouldn't be something I would do because I already know that the rifle and the sight are capable of making shots out to the practical limits of the cartridge the rifle is chambered for. Since I have probably fired somewhere around 10,000 rounds using this dot sight, there would be no playing around. I know where to put the brightness setting and seldom mess with it. I have never hunted with a dot optic, but looking back on the big games animals I have taken this would have never been an issue. I shot them all in pretty normal daylight conditions at ranges closer than 100 yards. This includes several elk and numerous deer. After owning both a scout scope (Leupold in Leupold QD rings), and a couple red dot optics, I would much prefer the red dot optic to the scout scope. I am sure others disagree.
If you are thinking of using either a dot sight or a scout scope I assume you are not shooting a benchrest match. You are trying to put a shot in the boiler room of a living target either in a defensive role or in a hunting situation. Either sight is entirely satisfactory for this. That being said, having the POI 1/2" or even 1" from where you would like the bullet to strike is not going to matter and even if it did, this is better than 99.9% of people can shoot in the field.