Yes Teazy 1st option is a lot more time consuming, by the time a person will pick the bails up and set em all back the batsman can come back from a nap and make his ground but technically the fielder does have the option to do that.
It’s not something very rare. You do see such incidence from time to time.
Sometimes bails are dislodged by the keeper or bowler by mistake while backing up and than they have to remove the whole stump in order to run the batsman out. It is understood that why they need to remove the whole stump off the ground.
India ended day 1 at 92/8, on day two they were all out for 98, NZ made 94 all out on day 2 and Ind made 154 all out on day two and NZ were 24/0 at the end of day two. NZ went on to score to win the match and clinch the series 2-0 in pathetic batting conditions.