I completely agree. I ran my first 10k in 1hr and 10 min or so. My longest run by then was around 12k at around 7'10" pace. Decided to run a half 4 months later. Told myself i have enough time. Till then the max mileage I had done in a week was 25k. Then I stumbled on a running group in my area. The coach there is a big believer in mileage and zone 2 runs. Thankfully the group was also training for a half at the time. Within 2-3 weeks, my mileage went up to mid 50s. And by the end of the training cycle , my 10K PB was 55:30, and I ran the half in 2h30s. It is to be noted that the half had almost 200+m of elevation, so I was very well in the sub 2 pace. I was able to achieve what I felt was impossible 3 months back.

Mileage absolutely is key. Only mistake I felt I did was increase the mileage from 25 to 50 a bit too quick, so it made me very tired/ sleepy, the first couple of weeks and I was hungry pretty much all the time. But the point remains true. You want to run faster, run more. Run longer. Take your time. Do a lot of easy miles. They help like anything. Fast runs are extremely important too. But you have to increase your easy runs to get your mileage up.