Going unbeaten in the league would be a huge achievement though and I hope he doesn't throw that away.
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.
True, but it's still something everybody will talk about and it's a title not many achieve regardless of whether it comes with any silverware or not. There's also no guarantees that Liverpool will win the Champion's League either, and if not, going unbeaten in the PL is something to add on to their domestic title. There's no reason why they can't go for both either.
CL will also be the next target after winning the EPL this season because the trophy title is in sight, so even if opponents are stronger than Liverpool they are still able to face it like last season and now Liverpool are stronger unbeaten in the domestic league this course will carry over to the next UCL match.