I also do this, in all bar three types of quests.
1) Powerlevelling runs - if I just want to level fast, I'm more picky in who I take.
2) End-game raids - There are times you need at least ten of the twelve to be able to pull their weight. Particularly in the Shroud.
3) Quests that can be ruined by someone who doesn't pay attention. Quests which can be failed because someone fireballs/heals the Venerated, or charms a must-kill mindless undead (Delara's cough cough), sticks their Finger of Death up at hostages (The Cursed Crypt), sets off really, really bad traps (Cursed Crypt again, can lose chests to this) or where everyone can get lost if they don't pay attention (The Shadow Crypt, Inferno of the Damned).
But my other favorite way to get a solid party?
Post an LFM where you have 4-5 melee toons, and accept any class, not just a cleric. Most bad players will not go on a quest with no Clr.