Tampa was a soft, underachieving team until their top players started playing dirty. Only point of getting a fighter is to show the top guys how to play in the league.
Some of Hughes, Bratt, Hischier, Mercer, etc. need to play like that. They'll be good at it also. Its not playing the body along the boards every time. Its the slashes to the shins when an opposing player skates by that gets you through the playoffs.
Tampa had their 2015 run to the Finals to give some good added experience to Stamkos , Kucherov , Hedman , Johnson , Vaslivesky , Killorn & Palat. All players who were eventually part of their back to back Cup wins.
Their teams in both of those Cup wins were just flat out stacked. They also have a great coach in Jon Cooper who had been their coach since the 2013 season. They learned the most I'm sure from getting swept by the Blue Jackets in the 2019 playoffs because they won the Cup the following year. The point is that it takes a few playoff appearances for the players to get comfortable and learn what it takes to win but at the end of the day you need the right combo of skill/depth/coaching/goaltending to get it done.
When I think of a similar team to Tampa who have had their share of disappointments in the playoffs it seems to be the Hurricanes.
Brind'Amour has been their coach for 6 seasons now and they have tinkered the hell out of that team over the years while keeping core guys around (Aho , Slavin , Pesce , Terevainen , Necas , Svechnikov , Staal). This year they have a good shot at winning it all but if it happens it's pretty clear that they didn't get things right in a matter of 2 or 3 playoff appearances.