While your logic is interesting, and most likely correct in general, all the practice in the world won't give anyone a guarantee of ten rounds in two inches in a personal defense situation. It is the case, however, the more you shoot the more you will be able to use "muscle memory" to get the job done. There will not be time to think.
There are no guarantees. Still,the chances of missing with a full magazine of 45+P if the only time you fired the gun was that one time at the range four years ago,is alot better than your chances of putting 3 or 4 or 5 rounds into a dinner plate sized area in an attackers chest from a gun,whatever the caliber you choose,that you practice with regularly. Whether they are .22 caliber or .45 caliber or anywhere in between,bullets that hit are far more effective than ones that don't. If you want to be able to land some hits on an attacker with enough reliability to protect your life, practice is going to be needed. If you want to miss,you don't have to worry about it. Most people,to spite what they think,are naturals at it.
I think it comes back to the advice of "Get the biggest caliber that you can control and shoot accurately". If money comes into play,practice is going to factor in to that biggest caliber. For that matter, if money is an issue,a 9mm is alot better than a 45 OR a 380 as far as controllability because the ammo is a lot cheaper,so your going to be able to practice more and get better at using it. The more I think about it,the more I think that a 9mm is the way to go if your on a budget,unless your not even going to be able to afford ammo for that,in which case a 22 might really be better.
My first choice for a cheap gun would the be the S&W sigma,or some of the Rugers. They go for around 300-350. I honestly hate the sigma. It feels awful, and I don't like their design of the trigger safety. I feel its a weak point and although I haven't heard of them failing,it just doesn't seem as strong as Glocks design (I hate Glocks too,but I admit they are great guns,I just don't like them) They are also DA only. Still,its a S&W and I expect that if I pull the trigger it will go bang,and I find when practicing (another reason to practice as much as you can) they will take care of it.
My next choice (actually,it WAS my choice) is the RIA 1911GI. It goes for about 400. (Actually,I shelled out 50 more dollars for the tactical,but the GI is damn good) I actually would not recommend my choice for others though. A 1911,even an expensive one is a temperamental beast. You need to understand that and accept it if you expect it to work reliably for you. (As an example,Wilson mags with Hornady XTP +P rounds work great,factory mags don't work well with hollow points and Gold Dots don't really work well in any mag)
Glocks are a good choice. They are not that expensive and damn good. Springfield makes some excellent weapons as well in that range. For the most part,Im just really worried about the Hi Point,they have such a terrible reputation. I want to see people saying they ran a few thousand rounds through it without any problems before I will accept its good.