Again - I don't disagree that the format is stupid. But also think you are exaggerating the impact. You are acting like Tampa basically has a bye - if the #8 seed is supposed to roll over for the #1 then someone forgot to send that memo to the Preds when they swept my Hawks 2 years ago. Or the other 6 times a #1 has lost in the first round. After Tampa - who is clearly the class of the East this year - seeds 2-8 all have between 107 and 98 points, and everyone but Pitt has 46-48 wins. That's pretty damn close to parity. This isn't Gonzaga-Farleigh Dickinson here.
If Tampa does squash Columbus in the 1st round, then no matter what happens in the next round there will be a canned explanation for it. If Tamps rolls in that one as well it will be as you described, where the talking heads say "the Leafs/Bruins beat themselves up in the last round while Tampa was fresh and took advantage." Conversely, if Tampa loses the explanation will be "they had too much time off - they weren't crisp. The Bruins/Leafs were tested in the 1st round and were able to keep the momentum going." People are very skilled at retroactively applying whatever narrative fits best.
Case in point - last year's Playoffs. Knights basically destroyed everyone - winning their 3 conference series in 4, 6, and 5 games (i.e. 15 total games). In the East, the Caps were challenged every series - 6, 6, and 7 games (i.e. 19 total games). If playing 4 extra playoff games really makes such a difference, please explain how the Caps steamrolled the Knights 4-1 in the Finals. I have an explanation - the Caps were simply better and it wouldn't have mattered if they had played 10 more games than the Knights.
I am lucky enough to have witnessed my team win 3 Cups in the last decade. I truly believe it would not have mattered where they were seeded in any of those years.