Regarding Klobuchar as a possible VP candidate; people generally dismiss VP candidates as not being relevant in elections. Mostly I think that's right: very few voters decide to vote for or against a ticket based on the running mate.

Additionally, given Biden's age, it seems like the priority this year (even more so than normally) should be to select someone who can take over as president if need be and/or who would make a good candidate in 2024. Biden also might look at uniting the party / exciting the base.

But there is evidence that running mates have some effect in their home states. In a paper Brenton Peterson and I published in 2015 we used synthetic controls to measure the average number of points VP candidates add at home as being around 3 percentage points.

Crucially, this holds true across different time periods and in states that are competitive and/or have a high number of electoral votes. So picking a swing state running mate can actually improve a ticket's performance (again, on average).

To be sure, the spread across individual candidates is quite big. So there's no guarantee that a candidate like Klobuchar will deliver. Additionally, there are not a lot of presidential elections that hinged on just one state.: in 2016, Clinton needed to flip 3.

But a 3 point change in Florida in 2000 or Ohio in 2004 would have put Gore or Kerry in the White House. And it's not clear whether Lieberman or Edwards added much else to the ticket (in either votes or potential governing experience).

Klobuchar may not be Biden's best potential VP, and there are good arguments for thinking about other considerations in selecting alternative options. But Biden at least considering a swing-state senator with a strong electoral record at home is very sensible.

For the article see; https://journals.sagepub.com/doi/abs/10.1177/1532673x16642567.
For more on the argument/approach, see: https://www.washingtonpost.com/news/monkey-cage/wp/2016/04/26/this-research-shows-that-vice-presidential-candidates-actually-do-win-votes-in-their-home-states/