I play on Lindblum too and train classes in your lvl range, and it's very rare for me to find a party which turns out to be a PL party instead of a normal grind party.
Like in..once every two weeks.
Maybe you just got really unlucky when searching for a party

Fights will always feel "kind of" slow (not in a party though..?) because FFXIV fights are not about "I can mindlessly click my opponent to death in less than two seconds!!1!" but about strategy: using the right skills at the right time, placing yourself at the right place, evading attacks, hitting for more dmg from the rear, etc.
That's going to be the case even more when we get player combos soon.
Get used to it. Not every fighting system is about speed.