Would Warbird make a good Avenger?

[The Roman Candle]

Sure. I like her well enough.

[Thudpucker]

Yes. Needs to go back to the Ms. Marvel name though.

[Dermie]

Every time she joins, it doesn't quite work out.

That's not true. The last time she served on the active roster it worked out just fine. She served for a good while, and was giving increasing command responsibility--and eventually chose to step down from active duty when she was offered the position of Director of Tactical Awareness for Homeland Security.
Yeah, she did have two prior stints with the team that ended badly...but her last term was very successful, and proved that Carol has what it takes to be an awesome Avenger. She should definately return to the team. That way Carol fans can enjoy her in her solo title, and as an Avenger, and as a supporting character in New Thunderbolts!

[Dermie]

Was that a retroactive thing or was that actually a part of her original storylines?

Neither. It was a development that came in recent years as a result of things that happened to her in earlier storylines. Carol has dealt with a LOT of crap over the years: her boyfriend was murdered by Mystique; she was kidnapped, raped and impregnated by an enemy; 'betrayed' by her teammates when they let her just leave with the guy, not realizing he was controlling her even though he admitted to using devices to make her fall in love with him; having all of her memories and powers permanently drained by Rogue; being tortured by aliens to unlock her genetic potential--which did end up giving her cosmic powers; and years later she ended up loosing her cosmic powers when the white hole that fueled them collapsed.
All of those traumas combined--plus the fact that Carol prefers to keep her feelings locked inside, rather than talk about them and work them out--overwhelmed her and she ended up developing an alcohol problem.

She eventually overcame it, when Tony Stark finally managed to convince her to go to AA. Since then she has not had any further problems with alcohol, and has gone back to having a successful career as an Avenger and as Director for Homeland Security.