All World War Two US tanks had live tracks, and they were designed to be run tight. Halftracks had tight track for a different reason--they were actually vulcanized rubber loops molded over steel reinforcements, and had no individual links at all.
Some postwar vehicles lack return rollers, so the tracks do sag, like the M113 armored personnel carrier family or the M109 and M110 series self-propelled guns. However, even here, the tracks don't actually run on top of the road wheels like a T-34 or Panther--they arc down and are supposed to be tensioned so they don't actually hit the wheels (though they sometimes do in service, at least at the center).