Every time I pure pug it I end up on a team with Tacs in Ambassadors and Odys.
See, now that's a problem of when you que. When the Que pops for ME, I'm always in a team with a mix of Tac and Sci, in BoPs, sometimes with a token cruiser, and the Feds are always some mix of lockbox ships and Kumaris, with a token cruiser.
Try queing sometime around midnight, PST during the week. That's when your side rolls out the good stuff.
"when you're out of Birds of Prey, you're out of ships."