I’m talking about last year, and while the roster was/is flawed, Boston was killing their 3 guard lineup. And again, why was KD their primary ball handler?
Did you see their roster last season?
They didn't have the personnel to match up with Boston on the regular. Claxton and Drummond were their only bigs and neither of them can stretch the floor, and neither are capable of playing extensive minutes against lineups which require switching. Kyrie and KD were the only ones who could generate any offense for themselves, so it's only natural that he would take on extra ball-handling duties to initiate the offense.
Truth be told, all those four games were winnable for the Nets, but KD failed to deliver down the clutch, so I don't know why you believe it was "bad coaching" as the reason for why they lost:
Game 1 - it was a one-possession game for the last nine minutes of the 4th quarter; Celtics ended up winning by one point
Game 2 - it was a two-possession game with three minutes remaining in the 4th quarter; Celtics pulled away late
Game 3 - it was a two-possession game with eight minutes remaining in the 4th quarter; Celtics pulled away again
Game 4 - it was a one/two-possession game with six minutes remaining in the 4th quarter; Celtics ended up winning by four points.
Or do you seem to think that the Nets should've played Claxton or Drummond during the dying stages of a playoff game?