This subject can be a bit difficult to address and there probably isn't a definitive answer that's going to satisfy everyone.
First of all, when you think about the 'average' firearm owner, it probably doesn't include folks who belong to internet firearm enthusiast forums. It's not exactly uncommon to hear how a surprising number of folks who own handguns probably still own the same original box of ammunition they bought when the gun was brand new, and there's still rounds remaining in it.
I once heard someone from a firearm company comment that marketing research indicated that the average handgun owner might not fire 500 rounds through their handgun during the entire time they owned it, meaning over the course of many years.
I have a copy of a report from a fed agency discussing testing of some service-type pistols back in the late 80's. In it is a statement that the average number of rounds estimated to be fired for training in the M9 at that time was 80 rounds per year. Also, a couple of the pistols with alloy frames being produced to meet military specifications for service life back then experienced cracked frames at 10,000 rounds (or less), but that wasn't considered unacceptable for military needs.
Now, as a firearms instructor and armorer I've had my fair share of opportunity to probably shoot more rounds than the typical non-competitive owner/shooter. I fired an estimated 45+K rounds through a single aluminum alloy framed compact I carried as an issued weapon for only a few years. I've fired many thousands of rounds through a number of other issued pistols, too.
I try to spread out the use among my personally-owned pistols. It helps reduce the wear & tear on my various guns, as well as helping keep me current with the different models I typically carry and shoot. I keep approx round counts for preventive maintenance purpose and I presently have 3 small guns which have seen in excess of 10K rounds fired through them. I've replaced some parts in them as recommended by the makers for reason of expected wear & tear of what's considered replaceable wear parts, and other parts whenever I've seen them exhibit indications that a parts replacement was in order. I don't consider any of those guns to be significantly worn out or anywhere near the end of their service lives.
I have some other pistols and revolvers which have seen even more usage over the years, too.
As long as a pistol is being properly maintained, meaning being kept clean, free of debris & contaminants and kept properly lubricated, I don't look at a gun being fired 1-2K rounds as being a "lot of rounds".
Now, if the gun had been abused and not properly maintained, and some accelerated wear, damage or even parts breakage might have resulted ... then even a relatively low round count might become a problem. Just depends.
Then, there are some pistols on the market which seemingly aren't intended to be fired as much as others.
It's still just a machine, you know.