I think you're overvaluing draft picks. You can't acquire multiple good players with a bunch of mid-round picks, unless they're A) soon-to-be free agent due a big raise, or B) significantly underperforming their current contract. Basically you can only make those kind of acquisitions if you have a lot of cap space to spend, which Tampa obviously doesn't.
Teams have no reason to let good, cost-controlled players go, especially to teams like Tampa that have only draft capital to spend. So if they're traded for picks only, it's gonna be a lot of picks.
Obviously, Jeannot wasn't worth that. But you don't have to squint too hard to understand why a guy that scored 24 goals in his rookie season, signed to a 800K salary for another year, would have a fair amount of value for a contender.