Do playoff wins matter if you don't win a trophy?
Yes. They matter in same way that regular season wins matter (as I said above) even if you don't win the Shield or succeed in the playoffs. It's not proportional, which is to say, making MLS Cup is not half as good as winning MLS Cup, but it's definitely better than losing in the Semis, or Quarterfinals, or whatever.
My Minnesota Vikings have never won a Super Bowl. In the 1970s, when I was a teenager, they made it to the Super Bowl 4 times in 8 years. They have not been back. As much as it hurt to lose 4 Super Bowls, the 1970s were easily the high point of my fandom with that team.
Three years ago they had an epic all-time final-play walk-off touchdown win over New Orleans in the playoffs, followed by an embarrassing non-competitive defeat to the Eagles in the Conference final. Nonetheless, winning that game against the Saints is WAAY better than the alternative even though it led to getting blown out the next week. The complete and unexpected joy that I and other Vikings fans felt after that last play against the Saints was real, and losing the next week failed to build on it, but did not make it meaningless.
If NYCFC had made 1 or 2 runs to the MLS Cup, or even the Conference finals, or some combination of those, there would still be a ton of complaints and whining and fans of other teams would never let us forget it. But that would be better than the record we have.