The second part of the video shows how to attach a new wing when a major portion of the original one is missing; for this you would need to get one of the spare wings you keep around the house...
Some butterflies are truly ephemeral, with a lifespan measured in days; for those species a repair would not be practical. Monarchs however, can live for six months; a repaired wing may allow it to fly from the Upper Midwest to Mexico. Whether it's worth your time and effort is of course your decision.
Looking in the youtube video comments, the "surgeon" mentions that the same butterfly has come back multiple times for repairs (which is amazing to me).
Obviously I don't know if that's because the repair job was damaged or if it was a new break. Either way, they're probably better off after the repair, even if it doesn't last the rest of their lives.
Just because it can fly off when released doesn't mean it doesn't then go out in the woods and die.
I mean, is there any evidence that six months later, some of these repaired monarchs could really make the flight to Mexico, etc? Are there instances of Mexican lepidopterists saying, "What the *#*$, there's cardstock on this dude's wing!"
Lepidopterophobia? I thought that I just coined this word, but it is for real!