Nope, it’s not just you. I think it’s true in football, too (not sure about the other sports).
Even guys who don’t go primarily by a nickname, but still have a well-known nickname (e.g., David “Big Papi” Ortiz, Frank “Big Hurt” Thomas) don’t seem to be particularly common anymore.
There’s Rowdy Tellez and Mookie Betts, but that’s all that comes to mind. Any other?
I’ve always found Gaylord Perry to be pretty amusing. I probably ought to have a much lower opinion of someone who cheated so blatantly, but at least he cheated with real style. He was having himself a grand old time while doing his very best to get on Major League Baseball’s last nerve.
Mookie’s first name is “Marcus” so I’m not even sure Mookie qualifies, it’s kinda just a play on Marcus. (This is as distinct from Mookie Wilson, whose real name is William, or Mookie Blaylock, whose name is Daron.)
Mike Trout is often referred to as the Millville Meteor.
The loss of nicknames is in part because sportswriting is different. Baseball is one of the oldest professional sports there is, so sportswriting about it started in the 19th century, when it was customary for language to be more florid and less direct; it might be written about a homer by Ed Delehanty that “the Gaelic strongman propelled the orb well above the Baker Bowl faithful” or some such wording. Accuracy and truthfulness were a guideline, not a rule, and so they’d changed quotes, or just make them up, to make the players sound more literate than they were. As writing was generally due on a next day basis, they had time for this approach; speed to getting things online wasn’t a thing. This is basically how sportswriting worked pretty far into the 20th century.
Basically, they had a lot of time for more verbiage, so the nicknames were created by the truckload, whether they because the guy’s unofficial name - Cool Papa Bell, Home Run Baker, Three Finger Brown, Double Duty Radcliffe, Satchel Paige of course, some guy named Babe Ruth - or a separate thing, like, of course, Bob “Death To Flying Things” Ferguson.
I suspect the recent dearth of solid nicknames is because sportswriting now is just way, way less literary, and more oriented towards just getting information out as quickly as possible. Still, they did just put The Crime Dog in the Hall of Fame.
I love nicknames. I wish we had more.
The Royals fan base has been giving their first basemen a series of related nicknames lately. It started with Billy “Country Breakfast” Butler, who got it from a sportswriter coming up with streetball nicknames for Royals players. Billy’s a big dude, and looks like the type of guy who’s ordering everything off the menu at breakfast. Billy retired after 2014, and the Royals signed Kendrys Morales. Latching onto his country of origin, fans quickly nicknamed him “Cuban Breakfast”.
Cut to 2022, and the eager arrival of prospect Vinnie Pasquantino. I’m not sure what fans were more excited about - his elite batting eye, or the even more elite moniker of “Italian Breakfast”.
For me, it’s a tie. But it sure helps that he posts about breakfast all the time on Twitter. 
He didn’t retire, he left as a free agent. Great nickname, though.
I think the best nickname in my lifetime was Garry Maddox, “The Secretary of Defense.”
If memory serves, it was a Royals first baseman who received the first moniker from ESPN’s Chris Berman: “John Mayberry RFD”
Best use of a nickname goes to either Dan Shaughnessy or Peter Gammons of the Boston Globe, I forget which.
Oil Can Boyd was observed returning some X-rated videos, which was dubbed “The Can’s Film Festival.”
Cal Raleigh, the star catcher on the Mariners, has the nickname Big Dumper.
It’s because he has a large butt.
By who? I live all of 50 miles from Angel Stadium and I’ve never heard him called that.
Mind you, I usually ignore the Junior League entirely, but still…you’d think I’d have heard.