I am no "Annie Oakley" and my handguns are way more accurate than I am. That being said . . . . I am always somewhat amused by reading posts on forums of "my gun isn't accurate" or "it doesn't shoot to POA so I traded it in", etc. For one thing, it all boils down to practice. In today's world, many of us use and own more than one handgun. Those who stick to shooting one or two individual handguns will usually be better shot with them as they have taken the time to "learn" their handgun - where it hits, what it likes best for ammo, etc. And let's face it - learning the correct hold and being consistent, learning the sight picture that works, etc. is very important. It's not a case of "can't", it's a case of "can" IF you take the time and patience to work at it. Yes, older eyes, weakening muscles with age, etc. all come in to play . . . but the important thing is to shoot the best you can and enjoy it.
Whenever I get a new pistol, I start out at close distances from the target and as I improve in shot placement, I then move back further. It doesn't come overnight. . . . and for me, my accuracy varies from one practice session to the next. I guess that's part of getting older. I no longer shoot in competition so the only one I have to compete with is myself.
When I got my first snubbie . . . I couldn't hit the broad side of a barn with it . . . but it improved because of practice and some advice on hold from a fellow at the range I was shooting at who was watching me. Itt's all a learning process . . . and telling yourself you "can".