Most people who want to learn how to shoot a handgun do so for self defense. They often don't want to carry a gun, but just have a gun at home for that midnight emergency. They just want to be able to stop that person from forcibly coming into their home. This is the person who buys a gun, shoots 25 rounds from it, loads it, puts it in a night stand, and thinks they now have a plan. If only!
What they are not considering is "the adrenalin dump". In a crisis, the human body goes into overdrive, causing massive physiological changes that dramatically impact the person's sight, hearing, reflexes, and motor skills. This can result in a pronounced loss in skills with a handgun, and sometimes, disaster. Where a casual gun owner might think that firing 50 rounds from a gun is enough to "get up to speed", highly skilled shooters will think 600 is just getting started. I often tell people that it takes 400 rounds just to break in a gun. Some handguns will jam often in the first 100-200 rounds, while a gun with 1000 rounds through it will usually be very consistent and reliable. "Usually" means, you get what you pay for, and a budget gun may not be reliable.
So, is becoming a more skilled shooter just a matter of shooting more bullets? That helps, but standing in one place and shooting at a large target with no time limits is not as helpful as taking a Qualification.
Qualifications, also known as a Course of Fire, are simply shooting tests. There are hundreds of these, and are required for many areas of the gun world. Easier ones might be used for acceptance into a private pistol club, or to qualify for a handgun license. Harder ones are used in law enforcement. Police officers at every level, armed security guards, body guards, Game Wardens, and armed Federal officers all have to qualify on their weapons 1-2 times each year.
I collect qualifications from different police agencies, and use them for myself and for students. Some are very basic (Ohio State Police), some are quite difficult (U.S. Border Patrol), but most are in between (Dallas PD). They all feature specific time limits, which puts pressure on you. The good news for you, is that, as a civilian, you don't have to pass any of these (unless you want a License), but you will want to. Working on some of these will give you real insight on the skills you really need, like gun handling, fast target acquisition, and transitions.
There is no reason a civilian gun owner cannot shoot as well as a cop. You can prove that.