The only time, I would support (not root for) a loss, that was strategically planned, is when the season is lost (no chance for postseason) and we know that the difference between winning and losing the last game will results in picking several picks later.
Remember it is not just the first round, it is every round.
If you sit a few starting players in order to protect them from a late season injury is that really tanking or is it making good business decisions?
Planning to tank an entire season, before it even starts, that is for forum meatballs, and no coach in the NFL wants to be viewed as the problem with the team.....