You're giving up more than a little by not splitting faces
In many shops requests for skill checks come from the floor, not initiated by the eye. In these cases then yes, developing a reputation as a moron is beneficial.
How would you know that splitting 10s will automatically bring down the heat if you're afraid to do so?
In those rare occasions where the casino shows it's throat, you can't take a little nibble with your 20. You have to clamp down, HARD, and re-split to 4 hands if possible. I am a regular 10 splitter playing chunky red and light green and get no heat. I even get away with it on a "counter trap" DD game I know many who have gotten the heave-ho from. To reiterate, these are local stores I play bi-weekly or so.
It's all in how you present it. I give up my EV in low bet situations to set up the correct play when the money is on the line. Refusing the 10 split is the opposite of that. A successful quad 10 split with a dealer bust can be enough to make a losing session into a winner, it has for me several times.
One last note, if a store will skills check you for splitting tens early in a shoe, they are overly paranoid anyway and you won't last unless you spend almost all of your EV hiding your skill.