I was breaking 80 consistently by the time I was 16 yrs old. I'm 56 now and my scoring has not significantly improved since those days. I went a few decades without playing much and I'm trying to get back to the low 70s.
I live and play in Japan and the courses here are difficult for me. They aren't long but are VERY narrow with OB left, right and over the green on almost every hole. I can score in the 70s without using a driver or even a 3 wood, just the utility (5 wood?). That or a long iron is enough for me with the tees almost always way up on the front of the box. (Very difficult to find lower handicap players willing to hit from the back). And the greens are often very undulated and fast. Very difficult to score sometimes even when hitting the ball well.
Anyway, I also feel that getting more consistent at the full swing and hit more GIR is the biggest key. That said, I disagree with one poster who discounted the importance of the short game. I've always had a better than average short game and relied on it heavily in course management. My thinking off the tee used to be: Get the ball anyway safe where I can get my approach shot anywhere near the green. From there I felt I could get the ball up and down.
As I've gotten older, my short game has fallen off, but I love practicing it and I feel that it has a direct carry over into full shots. Of course there is the mental benefit of not being afraid to miss greens and feeling that you can get out of trouble. But I also feel that there's a bigger connection between the two than the other poster implied. One could think of short game practice as another kind of variability training. I know that there are all kinds of short game techniques but for me 90% of all my chipping and approach shot are just variations on the cut shot or fade, which is just a variation on the full shot. I think they're all connected.
On the benefits of variability training https://www.washingtonpost.com/news/wonk/wp/2016/02/12/how-to-learn-new-skills-twice-as-fast/?utm_term=.286eb9e9fae0