Jamin, you are correct that height is one of the most influential variables at play. Those denying that are...in denial.
But the influence if height varies depending how far below the norm you are. A long way below the norm - I'm guessing here but at say < 5'3 or 5'4, height may be the most influential variable. Most guys below that mark would be in the 'instant disqualification zone' for most women, regardless other strong features such as attractive face, teeth, build, haircut, dress-sense. Perhaps only significant money or fame, if possessed, would be able to outweigh a sub 5'3 height. Of course there are always outliers - I'm talking in general here.
What has surprised me though, in my experience, is how quickly the relative influence of height as a variable seems to diminish as you move toward the norm. I believe my experience is a fairly useful case study - if I stand up really straight on a good day I'm 5'7, and in my mid-twenties, I was fortunate to quite substantially improve some of the appearance-related variables over a short period of time - about a year.
Cue 'transformation story': I stopped running competitively and gained 20lb of muscle, enough to at least meet the 'soccer player' benchmark. I grew a (nicely maintained) beard, which improved the appearance of my face by a surprising amount - bye bye babyface, hello appearance of strong jaw (should've done this years before). I started getting my hair cut to suit my face shape. I threw away any clothing that didn't fit me perfectly, and replaced it with stuff that fit, and that complemented my now broader shoulders and chest. I stood up straight. I wore (minimally) heeled dress shoes and boots for a height boost. I used whitening toothpaste (orthodontics as a teenager meant my teeth were already straight). In short, my appearance improved probably from 5 to 8. One thing that didn't change was my income, which for this case study is useful as it helps isolate the effects of the appearance changes.
Having maxed my appearance, the difference when it came to women was MUCH greater than I would have thought (if I'd known, I'd have given up running and done all this so much sooner). Evidently, 5'7 is outside of the 'instant disqualification zone' of way, way more women than I had thought, provided you're strong on other variables. A note on social skills and charm: now that I look a lot better, women (actually, people in general) seem to perceive me as more charming and socially skilled (I'm sure my growing confidence also helped, but the confidence comes from increased success, not the other way around).
Now, some of the other bozos posting on this thread about being 5'7 and "never having trouble" are full of it (unless significantly wealthy/famous). Those guys have obviously not attempted to pick up tall hot women. I'm not slaying tall models every weekend. But I now do quite well, better than I had ever imagined given how poorly I did before.
I know if were, say, 6'0 or above with all other variables held constant that my success would be multiple times greater again, but Jamin man I encourage you to at least max out the variables that you have control of and see what happens. I hope you see the benefits that I have.