As far as I know that’s how all driving instructors teach it. The problem is, it’s much easier said than done. (Granted everything is, with the possible exceptions of selling seashells by the seashore and picking pecks of pickled peppers.) Also, different cars have different turning ratios. My VW turned tight enough that I would have hit the corner of the parked car’s rear bumper with my passenger door. But it never mattered, because in 40 years of driving, I can’t remember even one time that I couldn’t find a space I couldn’t just pull into.
I mean, of course, that I’ve never failed to find a space I could pull into.
Nope. I can do it, but not easily.
I don’t often need to, though. I live and work downtown - my car is pretty much only used to get me places I can’t bike or take transit to, and such places invariably have parking lots.
Better than lining up the front of the car is lining up the rear axles. This takes more of the difference in car lengths out of the equation.
I am very, very good at parallel parking, or at least I was when I had to do it every day. What I’m not particularly good at is judging the space I’m going into.
So…I can get into a space about six inches* bigger than my car. But the cars I park between are not fans.
*Okay, maybe a foot. Not good at judging spaces.
I do it from time to time. Maybe every couple of months. I’m OK at it, but not great.
(My wife, who drives a lot more than me, is very bad at it. I think this is mostly because she’s afraid to try.)
I do it every day but I still pretty much suck at it. I always look for those two spaces together so I have the extra room getting in.
When I was 16 my dad said I could parallel park anywhere. 50 years later, I can still do it but I don’t have to do it very often now so I’m not as good at it as I used to be.
I’ve parked in spaces with negative clearance (meaning they were smaller than my car) on at least two occasions that I can remember.
On another note, you know how you sometimes see these pictures of dying animals with vultures nearby waiting for them to die? A couple of months ago I was in a crowded neighborhood and came up to a guy trying to parallel park and I could see at a glance that he wasn’t going to fit in that spot - and that my smaller car would. So I waited. After a bit the guy gave up and drove off, and I slipped right in. 
This is basically the technique. I rarely have to parallel park but have no trouble when I have to.
Watching other people, I think the biggest problem is not not understanding a basic principle. Your steering wheel controls the front tires, not the rear ones (unless you have some weird car). Getting the non-steerable part of the car into the proper position is key.
If you see someone go nose first into a spot, they likely will have trouble.
Bonus questions:
Have you ever parallel parked on a “gracht”?
With a van?
With a van on a gracht?
Almost all the street spaces in our town require you to parallel park so when we’re parking our car on the street there’s constant practice. However we currently park our car in a rented space in a garage building and only street park our son’s car when we’re looking after it (moving it around to avoid weekly street cleaning hour). Other people doing it as often might be better at it, but I know a lot of people almost never do it and some are comically bad at it. I see some of them, visitors trying to park in our neighborhood. On our street the open width between parked cars on each side is <twice the width of a car too, so you can swing the nose out too far and hit cars on the other side of the street. 
I find the backup camera to be helpful in parallel parking, as well as where the side mirrors point down automatically when you put the car in reverse. Our son’s car doesn’t have either though.
I’ve never owned a vehicle with a backup camera.
Yesterday I sold our old pontoon boat (yay!) and I stood in front of the trailer, giving hand signals for how to turn and how much room he had left. He backed up flawlessly. I was thinking it was 50% me, till he told me he was watching it on his dashboard and never once looked at my gesticulations.
I really miss my backup camera when driving someone else’s car. You do have to be careful not to rely on it solely though, you can easily miss important things if you don’t have a general look around.