The pets themselves are pretty much the stats of 1-13* weapons. They even have their own potentials too.
Tacts are the only way to set a pet and their pas to weapon palettes.
We cannot extend them to prevent multi-classing as a way to limit pet usage to Su mains.
There's no doubt about it that they're purely cosmetic.

Stacking the stats of a pet and a tact that actually has good stats would seem rather ridiculous.