How to attach a potentiometer to a servo motor shaft

Why does it matter to a servo whether the command is relayed over a remote control system?

Reread the previous post. Nobody said anything about remote control.
The wording used was "Radio Control"
If you have never used radio control then perhaps you should Google "Radio control servo"

If you are an experienced radio control hobbyist then you already know that the arduino uses
the Servo Library to talk to RC servos and also that RC servos are a specific form factor
that uses RC servo "Arms" that plug onto the servo shaft. If, however the servo is NOT
RADIO CONTROLLED (at this point it is irrelevant that radio control is in fact a form of remote control since the discussion is about form factor and programming) then the term "servo
motor" means something completely different, which I might add, your typical RC hobbyist
would have no experience with , since a typical industrial servo motor costs hundreds if
not thousands of dollars, especially if equipped with absolute encoders. Even the ones
with incremental encoders are expensive.

RC SERVO

AC BRUSHLESS (NON-RC) SERVO

So, in conclusion, the difference between "RC" (which stands for RADIO Controlled, NOT REMOTE controlled) and "NON-RC" is the difference between $16 USD and $622 USD.

So yeah, it does make a difference. It's not about whether it is REMOTE controlled or
NOT REMOTE controlled, it is about WHAT KIND of SERVO we are talking about.
If we were talking about RC servos, (which we are not) then we would ALSO be talking about the SERVO library which , (as already pointed out) takes a position argument in the command so you know WHERE (what position) you are commanding it to .
If , on the other hand we are talking about industrial servos, then knowing WHERE the shaft is requires a whole other approach, hence the OP's request for a way to couple the motor shaft with the pot shaft

So if you have this:

INDUSTRIAL AC SERVO MOTOR

you can couple it to this:

POTENTIOMETER

using this:
SHAFT COUPLER

There is of course the caveat that you must write you software to NOT allow the motor
to attempt to drive the pot PAST the END-STOP.

And just for the record, we have not yet discussed AC vs DC regarding servo motor type.

It is unknown at this time whether an adaptor will be necessary since the pot shaft diameter and the motor shaft diameter remain unknown.

hat just doesn't make much sense as you always know where a servo is: at the position you tell it to go

Clearly this is a reference to an RC servo since nothing has been said about absolute encoders or incremental encoders and the OP's first post is clearly a statement of intent to build a closed loop system which he obviously wouldn't need to do if he had an absolute or incremental encoder, so no
he doesn't yet know where the servo is because he doesn't even know what kind of servo he is going to use, let alone how he is going to get feedback. (although he has a theory about that)