It's not strictly an emotional argument, though the "emotional fan" perspective is important as it's the fans that will be the ones purchasing the tickets and providing the franchise with that source of revenue.
It's also grounded in some degree of reason and logic. Good teams need to lock up their best players before they hit free agency. I'm not naive enough to think that they'll be able to lock up all 3 of Burnes, Woodruff, or Adames, but extending one of our pitchers in particular would be wise considering how crucial ace pitching is to a successful World Series formula and the general lack of high-level pitching talent in the farm right now. I have yet to see a convincing argument that the payroll isn't there for at least one upper-tier extension.
We may not be the Dodgers or Yankees, but we're also not the A's/Rays either due to consistent strong support from the fanbase. Keep making moves like this, however, without subsequently reinvesting in the roster, and fan support will dwindle and we will become one of those teams.