This may sound like a cop out, but it depends on the table.
On my Michell Gyro SE, it absolutely sounds better (to me) with the Michell clamp.
With my Pioneer PLX-1000, record weights and mats do indeed change the sound. Is the change an improvement, or just different? Lately I've been preferring the PLX without a record weight.
I agree that the use of a clamp depends on the table (and its design).
Adding an AFTERMARKET clamp...
can increase the rotating mass, but at the same time increases the bearing load (more wear, noise)
will most likely disturb the balance of the spindle / platter assembly and increase run-out (will never have an exact, dead center fit on the rotation axis unless specifically designed to work with the table)
will press down on a record, (might help with warpage, depending on the shape of the distortion) but will also increase the compression of the mat (more vibration transmitted to the record)
won't help with lateral tracking (e.g. a record with off-center or oversized spindle hole), unless its slipping and shifting while playing.
IMO, Best not to add an aftermarket clamp, as cons may out weigh the benefits.
edited: or use the type that Schiit demonstrated with (preferably of low mass to minimize bearing loading)