Here’s fine load of 1971 (I think) Mopars, and a highly diverse collection. Crickets from the UK, Colts from Japan, and of course a couple of domestic ones too. And even the truck is a Dodge.
And here’s one from several decades earlier, with just domestics on board:
This looks like Dodges, and once again, the truck is a Dodge. Car carriers have always been independent contractors, but there clearly were terms that resulted in the semi trucks often being of the same manufacturer as the cars being hauled. That was more often the case the further back one goes, and less so in more recent decades, until nobody cared anymore. The domestics eventually all ditched their heavy duty truck lines, so that made it impossible. And the great majority of imports didn’t have trucks to use.