The only case that could be made for bringing back the core is: regular season excitement.
There's a large enough sample size to realize this core, as constructed, does not have the heart, guts, versatility, and attitude necessary to win anything significant. They have proven that.
However, for 82 games this core is exciting, dramatic, entertaining and fun to root for. In terms of raw talent and pure skill, it's been decades since the Leafs had an offensive core capable of wowing us offensively. They just don't have another gear physically or mentally come playoffs.
It's also likely that any trade involving the core 4 would end up being a "loss" on paper and in terms of excitement. There's no way the Leafs could parlay a Matthews or Marner into a Draisaitl, Tkachuk, McDavid, MacKinnon, Pastrnak, Bedard, etc. So any deal they make would likely be a depth deal that returns better "team players for the playoffs." But those trades don't end up being sexy unless you win a Cup.
Those in charge of the team are likely subscribing to the "bird in hand" mindset. And this core, sans Tavares at this point, are so tantalizing that people can't help but wonder, "is this finally their year?"