He's kind of limited himself by promising to have a woman as VP. I won't be surprised if it's Warren. That would actually help him with the left. She's already said she would do it, if asked. Klobuchar probably gets him more Northern swing states. She's also a lot closer politically to Biden.
Warren wouldn't help Biden get to 270. The Northeast is going Democratic whoever Biden chooses as is the West Coast. I would think someone who could deliver a state Trump won in 2016 and have a positive influence in swing states in flyover country would be much better than an old woman, Warren.
Warren probably would hurt Biden in some swing states. Hillary won Minnesota by a single point in 2016, a Klobuchar would guarantee Minnesota stays blue and help in Wisconsin. Baldwin, Wisconsin would deliver that state to Biden, help in Minnesota and Michigan. Whitmer, Michigan would turn Michigan blue, help Biden in neighboring Ohio and Wisconsin. All states Trump won.
Abrams in Georgia wouldn't guarantee a win here. But one must remember she lost the governor's race by a mere 55,000 votes. She's a good campaigner, there is probably around a 40% chance with her as Biden's VP, Georgia could be won. I'd give Masto, Nevada a good hard look. Hispanic and ensures Nevada stays Blue. Masto could deliver Arizona to Biden and would have heavy influence in Texas.
All the above provides regional balance along with helping Biden get to 270. Warren neither helps Biden get to 270 nor does she give the ticket regional balance.
I'm a numbers guy, ideology means little to me. The idea is to get my candidate a win. Warren won't help in the midwest nor the south. Harris has been mentioned, but California is going blue anyway. it make no difference whether Biden wins California by 3 million or 4 million votes.
If I knew of a good candidate from Florida or Pennsylvania that could deliver those states, I'd go with them. You're talking 29 and 20 electoral votes and both states Trump won.
I'm not sure if I can say that you are definitely right, but, I don't think you're wrong when it comes to Kloubachar. If I had to lay money, it'd be on her as the wisest choice.
I do think that, in a country dealing with a crises (and likely still dealing with its effects come November) that Abrams may be a weaker candidate than you depict - people tend to lean towards experience in higher-risk scenarios.