If what Klopp is referencing is true w/r/t having received a memorandum last April from the Premier League imploring teams to respect the winter break, not scheduling fixtures during this time, making it a real break etc, I don't fault him at all for calling the FA out on this. EFL fucked Liverpool over once this campaign with the Villa tie in the Carabao Cup being literally the day before the Club World Cup semifinal. Klopp obviously had no choice but to pick one of the competitions.
The FA is preaching that all clubs have full dedication to its competitions, but is the guiltiest of all major football associations with fixture congestion given the 3-in-10 days setup during the festive period while nearly every other major league in the world is on break. Sam Ricketts
doesn't seem to have an issue with Klopp's approach either, though he has a little bit more to gain if Liverpool field their U23s. The bottom line for someone in Klopp's position, at least IMO, is that there's a constant take with no give for his players.
The quality of the squad means many of them are called up for continental and global competitions that take place every other year. Players are at that point out of his control, and not infrequently out of commission - see: Keïta essentially having his fitness abused by Guinea's then-manager Paul Put. During nearly every break in league play, there are one or more qualifying matches for said competitions. In the course of this Liverpool campaign alone, they've had matches across 7 different competitions - PL, CL, League Cup, FA Cup, Club World Cup, Super Cup, Community Shield. Including preseason fixtures, Liverpool's squad have played 48 matches in ~6 months (just under two per week), with at bare minimum 16 more to play if they don't progress in CL or FA Cup. In addition to these club competitions, players like Firmino have played up to 15 matches for their country in a calendar year.
Given Liverpool's PL and CL positions, I can't fault Klopp for valuing an already-promised break for his senior squad over an FA Cup replay. Maybe the solution is to buy £60m squad players like City so they can rotate properly.