But the FA or UEFA doesn't give you any extra awards/silverware for going unbeaten in the league :/

The EPL title is already a massive achievement for Liverpool, but their next target should be winning the CL (back-to-back), not becoming the new "The Invincibles". Going all-in on the unbeaten run (as in being afraid of dropping points so they field the best starting XI vs Norwich or any other team three days before a CL match) would look to me like Klopp & Co are being tryhards.