I'm going to offer a different perspective here.
Players cards do indeed provide casinos with your personal information. Using your credit card at a casino does too, and as we all know, many casinos share their database information...so chances are, unless you're cash-only...you're anonymity is a thin illusion at best. If a casino wants to know who you are, then they'll probably be able to find out.
More to the point...aside from massive bet spreads and bold ten-splits, WHY would a casino want to know who you are? Is winning a good enough reason to get tracked? I'm going to suggest that winning alone isn't usually enough (clearly some cases are going to draw heat for their own unique reasons..large amounts, etc.). Why not? Because even if the casino has an undeniable 5% edge over the player....45% of the hands played will still be player-wins. Meaning that at any given time...almost half the people at the tables can be winning and the casino is still bringing in cash. It happens. People win. Casinos know that their statistics guarantee that they will win slightly more often...but not all the time. Casinos WANT to have winners. A winner at every table draws six hopefuls to the remaining seats.
So, if winning alone isn't good enough to merit scrutiny...what then?
How about acting shady? The pit boss sees a player laying down chips for a few hours, they look like they're having a "good streak"...the casino has a vested interest in keeping that player at the tables...because eventually...that player will succumb to the casino edge. So Mr. Critter saunters over to the table to offer a Player's Card...to amass comps...free stuff. The player dodges the question...apparently, this player is the only person in Las Vegas who hates free stuff.
If I were that pit critter...I'd keep an eye on the player. By rejecting the Club Card...the player is waving a huge red flag that has bright yellow letters on it reading, "I'M DIFFERENT THAN OTHER PLAYERS!!"
Now...a slot machine can keep tabs on every penny in and out of the machine...every play you make...every push of the button....but a table isn't a slot machine. When they swipe your card (Someone correct me if I'm wrong) and log your play, they don't care what you win or lose...they are entering your bet-per-hand. Comps are based on a percentage of what you put down on the table...not what you take off of the table. The pit boss simply doesn't have the time to monitor and enter your win/loss ratio...And even if they come by to check out your ever-growing stack of chips....nothing is stopping you from coloring up a nice stack of red into a pocketable black chip.
So...I always get a player's card. It's good cover...I'm just one of the many...looking for a free buffet. I actually enjoy getting comped. And nothing is stopping me from NOT giving my card to the dealer when I wong in to a hot shoe, preserving my "anonymity" and giving me the perfect "out" when the pit boss comes by to scope me out. ("Sir, can I interest you a Club Card?"..."OH! I already HAVE one...I forgot to put it down...thanks for the reminder...hey...is this a good time to hit the buffet? Maybe you can help me out with a meal comp...this is my sister's first time to Vegas, and I just lost a grand on Keno...").
Etc. Etc.
Basically...I think there are valid reasons to NOT use a Club Card at many of the places you go ...but there's no reason to avoid signing up for a few. Plus, nothin' beats a lobster dinner for the price of the tip.
Being a man at the tables I'm assuming is probably more difficult and the type of single man I am probably got me 86'ed just because I've flirted with the ladies some in my past. Gotta worry about the "envey factor" too as man. The male pit boys just can't seem to keep the ladies interested in themselves while I'm in the loop. I gotta fight everything ya know, ....... sucks big-time.