Yes, this is what happens when a team coasts through the regular season and ends up with a lower seed. There's no bonus standings points for being a 2-time Cup winner.
If the playoffs were 1v8, Tampa would have most likely faced NYR, then FLA, and then CAR (or possibly TOR) - so same thing, different order. If you want an "easier" trip to the finals, then play harder in the regular season.
Unless you're arguing for 1v16, in which case, good luck convincing NHL owners who have to pay for the extra travel, the NHLPA who have to suffer through the extra travel, and the networks who have to deal with worse ratings due to East vs West time zones making a mess of start times.
On top of that, do fans even want to deal with East vs West starting right from round 1? Away games possibly starting at either 4 PM or 10 PM? Yuck.