I never even thought of stocking those for team ups.
Spoit - you're probably the most specific with your asks. Who do you typically want? I'm usually sending 3* DP, 2* OBW or a covered 4* like XForce or Flaptain. I typically don't send HB because his red drains your stock and his black self-damages.
None of my 5*s are over 4 covers so I don't bother.
I made a big post a month or two back, but speaking generally? Utility > damage. Stuns (MBW really is head and shoulders above everyone else at that), AP generation (OBW, GSBW, etc), and board control (JG purple, juggs, etc).
Otherwise, AoE damage is nice for lower level content, like blazing through DDQ. JG or DP are the best for those, because of their secondary effects (the boosted special tiles from her green are especially potent this week). Failing that, low AP 'poke' moves like DP or HT's red, or 4cyke's blue are more useful than slow, powerful ones. Since those you usually have other people on hand to boost the AP gen for. In your example, flaptain's yellow (as one of the only good protect/AP ratio moves) is way more useful than his red (which is really kinda mediocre without his yellow spamming the protect tiles in the first place).
But really, I'd take any random 3* or moderately covered 4* over 1 cover 5*s that do pretty much nothing.