Depending on how hardcore one goes in for a specific player and how popular that player was, I think the idea that nobody else collects them is unlikely. I also realize that it was probably not meant literally. 1000s of people collect the very best players like Jeter, Griffey, Trout, etc. Fewer yet will collect popular, star players that might be a bigger regional draw. Some guys popularity transcends their career numbers/stats and other guys may have a single draw to them such as a story or an event, in which case you are again probably not close to being alone.
I look at it this way, if you are collecting someone who no longer plays and did not have much in the way of a career or was very under the radar, then you may be one of the select few who are collecting that player.
I can say that I don't fall into that category, simply because my collecting interest & budget does not support run of the mill guys. That is not to say that I only collect highly popular stars. I would need a strong personal connection to a lifelong common to even consider collecting them with any sort of passion because otherwise I see it as a waste of money and I don't have that with anyone. Perhaps the closest I came was collecting all of the Brock Stewart cards from when he was in the Donruss Chronicles set, at least I think that is what it was called. Stewart was a 4 year career guy, from 2016-19 and had a lifetime record of 6-3. I only did it because he was a Dodger prospect though, and I collect all Dodger autos. This was his first auto offering, but after grabbing several low serial numbered cards for relatively cheap, I decided to see how many different I could get in hopes that i'd luck into buying a guy who had potential to explode in popularity. I guess the affordability should have been my first clue! However, he left the team in the middle of 2019 and after completing as many different cards from this one set, I was done. He went 4-0 with Toronto to wrap up the 2019 season and has not pitched in MLB since. I did similar exercises with a couple other guys (Jose Fernandez & Tim Locastro) then decided that was a fools game to play. Oddly enough, Locastro set a MLB record in 2021 for most SBs without getting caught to begin a career (28), but otherwise has not done much to brag about. Tim Raines was the previous holder of that distinction. I can't find if Locastro extended that streak or it ended with 1 more than Raines though. That is how odd and obscure the record really is.
My more "obscure" player collections that I have put more than just a basic effort into, although I don't even begin to think I am alone, are Willie Davis (60s/70s Dodgers) and Al Oliver.