@ Moffy,
I don't know where you found that 'caveat', but it is nonsense, having checked with some other engineers, none of us have ever found this to be true, the wiper contact is not current dependent. I have pots in circuits that have not been tweaked in years and they are still working just fine. As an example, the HP3456A is full of trimmers and they are quite stable after being untouched for years. If they are a bit 'creaky' after being readjusted, just rotating the wiper back and forth a few times restores complete functioning.
A lot of trimmers are used in my primary resistance bridge, they have been stable and work just fine after decades. I have not found any mention of such problems in the literature from trimmer/pot manufacturers including detailed handbooks on the subject.
In wire wound 'pots', it is the wiper that causes the higher TCR, it is a combination of the alloy it is made out of and the contact variation with the resistive element. Reducing the current through the trimmer effectively reduces the TCR effect. In other 'pots' with higher TCR resistive elements, the TCR of the wiper becomes less noticeable as it tends to be less than the overall TCR of the element, reducing the current in the wiper will still have the same effect though.
It is the selection of the correct pot for the application which is critical (when needed), it should be chosen for best resolution, minimal self heating, noise and TCR, it all depends on the circuit's requirements.