'Set pieces' have to my knowledge (over 60 years of supporting the Reds), never been given a high level of importance in United's training/coaching play-book. This is principally I suspect because we believed only inferior teams relied on such situations to engineer winning positions.
The famous quote (or possibly it was paraphrasing) from Sir Matt when asked about the secret of football management he was reputed to have said "With players such as Best, Law and Charlton you just throw them the ball and say go out there and play, with players like Nobby (Stiles) you say... go out there and win the ball, then give it to Bobby". That was as much thought to 'set plays' as was probably ever given!
Practicing set pieces was the 'journeyman' approach to playing football, we were not journeymen we were a team of stars, we still believe we are and so even when the evidence is staring us in the face there is a reluctance to accept that being proficient at taking/defending corner kicks, or free kicks, or even taking time to practice throw-ins especially in the final third of the pitch, is a worthwhile use of time on the practice pitch. Practicing even the 'set plays' arising from defending situations, like in reacting to a strong press, covering break out spaces, etc. all seem not to happen, indeed at times you could swear that half the time our players seem as though they train on different pitches, so clear is the lack of understanding/anticipation of what arises from 'set play' positions. How many times have so called quick free kicks been taken, supposedly to catch the opposition flat-footed, when the player receiving the ball unexpectedly has a look on his face that says 'what the feck have you given it me for?'
We are getting better at many things, but some of the basic set play positions are still giving grave cause for concern... but no one outside of fans, seems to understand or even care!