I'm not disgreeing with any of these opinions, but I'm just going to present another viewpoint. Lower magnification scopes are much more likely to allow a clear, in-focus view of the target at closer ranges. I've used 2.5x or 4x power scopes on some light .22's for plinking use and have had some that focus as close as 25 or 30 feet. I have an old Simmons 2.5x scope that is marked as a shotgun scope...it cost maybe 30 bucks about 18 years ago. It lived on a slug shotgun for years, so it's fairly durable, and it is now one of my favourite scopes for close-range .22 use. The image is crystal clear at 20 feet.
Parallax? Parallax exists only when your eye is not centered in the exit pupil of the scope. Most centerfire rifle scopes are parallax-fixed at around 150 yards...BUT...if you can maintain your head/eye position relative to the scope so that you are always seeing a nice, round field of view, without any image cutoff around the edges, you will not have excessive parallax at any range. Parallax is the apparent movement of the crosshair on the image caused by those two elements not being focussed on exactly the same plane within the scope...but if your eye position is correct, it doesn't matter how far apart the two focus points are...there is no parallax.
If the exit pupil...the "tube" of light that the scope transmits, within which your eye must be placed to see the full, round image...is large enough, your eye position can vary a bit, up, down, left, right, and you will still see the whole, round picture. You might get a bit of parallax in these cases, but it will be a fraction of the maximum parallax that can exist. Check the scope specs to find out what the maximum parallax is (it's not a huge amount), then consider that by keeping your eye within the exit pupil, i.e. centered, you will get, at most, only a small fraction of that maximum value.
Right about now somebody will start to comment (usually sarcastically) that this critical positioning is easier said than done, blah, blah, blah. I'm not saying that it is always done perfectly done, but it's just good form. With practice and a gun/gunstock that fits you reasonably well it's not at all difficult to place your eye corrrectly each time. It's a natural inclination to center your eye to get a good, round field of view. Just do it as well as you can, consciously at first...it will soon become second nature and done without conscious thought.
High magnification scopes at close range? Adjustable parallax, for sure. But "upgrading" all your scopes to AO? I hope that you're not a hunter...for target shooting, maybe, but in the field it just isn't always practical to be spinning focus dials/knobs all the time.
Just my opinion based on experience, and worth what you paid for it, like anyone else's.
John