I don't know about anyone else but, I feel I want to learn how to do things properly before going and modifying the gun to fit my current improper technique. There's always the possibility the sights are physically misaligned, though you'd have to shoot properly from a rest to determine that. Personally I see it as you can modify the gun to fit your bad habits, however you will still have the bad habit and should you pick up any other gun that has not been modified to compensate, your bad habit will still appear. What if you get in a self defense situation and for some odd reason have to grab a gun that hasn't been modified to compensate for your bad habit, then you are going to have the same inaccuracy and that's certainly not good. It pays to learn much more than it does to modify your gun or make up for a lack of skill by adding all sorts of expensive match grade stuff to it. Personally, I still have some problems with trigger control and still tend to shoot a bit left. A few months ago, I was sometimes shooting pretty far left off the bullseye, like maybe 6-10" shooting off-hand even at 7-10yd's (hey I'm still relatively new to handguns). I should also mention that I'm cross dominant meaning I shoot handguns with my right hand and am left eye dominant so that could likely be a part of it. However, for right handed shooters, typically shooting anywhere to the left usually has to do with improper trigger control (yanking, too much trigger finger). One thing I've noticed is that, while I've been focusing on proper grip and trigger control a lot lately, my groups have slowly become more and more consistent, tighter and closer to the center. Now I usually tend to shoot dead center with a few off to the right 1-3" though usually still in a "tight" group. Slowly I think I'm improving though I think I still need some work on the trigger control and I really need to start working out my hand and upper body strength as well so I can be a little more consistent. It takes time and practice. Get some snap caps and practice dry firing. Also one technique is to have a friend load your mag while mixing some snap caps in to see if you end up pushing/flinching when you reach it.
I would also recommend focusing on one technique at a time. Judging by everything I've read from the experts and sort of learned on my own is that trigger control is vastly more important than most people realize, and more important than grip, sights, etc. The reason being moving the gun only a very few degrees any direction at the muzzle as a result of yanking the trigger, too much trigger finger on the trigger causing a pull at an angle....those few degrees equate to significantly larger groups once you factor in the distance between the muzzle and the target. I'd really recommend experimenting for beginners. Try out different grip holds, try out different stances, etc etc. Find one that still gives you proper control, but is comfortable to you. Though, focus on one technique at a time IMO because if you start trying to work on different grip holds and working on your trigger pull at the same time, your improvement might not be as noticeable, and/or you might not improve as quickly. I'm not saying necessarily you have to perfect one thing first before you move on. I'm just saying pace yourself. Force yourself to focus on nothing except trigger control for one 50rd box, grip for the next box, or break it up in days instead of boxes or whatever suits you. Once you separate training individual aspects like that, and once you actually start to see the improvement in groupings from relatively minor changes, believe me, for most people things are just kind of going to "click". It will make a lot more sense, and you will likely start improving much more quickly once you've actually experienced this improvement and physically understand what's going on as opposed to just reading about it on the internet. Man I think I'm starting to sound like an infomercial. lol
One technique that REALLY helped me out was what is called surprising yourself with the trigger. Trigger feel, pre-travel, over-travel, etc are different on most triggers, however the basics are the same. What you do is slowly ease on the trigger and take up the pre-travel until you reach the sear trip point (don't pull past that yet). Once you've taken up the slack, keep focusing hard on your sights and the front sight and don't even think about the trigger. Just slowly keep easing on the trigger and eventually you'll trip the sear and the gun will fire sort of surprising you in the process (it's important to do this slowly and focus on the sights for it to be effective). After firing, do not release the trigger all the way, simply release until you reach the reset at which point you should hear an audible click of the reset or sometimes you can actually feel the minor vibration through the trigger and frame. Rinse and repeat as desired.
The whole idea of this training method, as I understand it, is since you are pulling the trigger ever so slowly and focusing on the sights it will help you to eliminate trigger finger flinch and focus on easing the trigger straight back in the proper manner as opposed to just yanking it. After enough time, practice, and experience speed will come.