Senator Elizabeth Warren’s endorsement of Joe Biden for President, which came on Wednesday morning, had little of the Sturm und Drang of the endorsement, two days prior, from Bernie Sanders. It also lacked the fanfare that accompanied Barack Obama’s lengthy salutation to Biden on Tuesday. But, in some ways, the home video that Warren posted on Twitter was the most effective of the three endorsements.

When Sanders appeared in a live-stream conversation with Biden, it looked like the digital-age equivalent of a battlefield armistice: two old warriors agreeing to unite against a common foe. Obama’s twelve-minute video seemed to be almost as much about the former President reëntering the political stage as it was about Biden. By contrast, Warren’s message was relatively brief—her video lasted about two and a half minutes—and it focussed primarily on Biden as a person.

After mentioning the former Vice-President’s middle-class roots and his long career as a public servant, Warren brought up the personal tragedies that he has endured and said, “These experiences animate the empathy he extends to Americans who are struggling, no matter what their story. Empathy matters.” Then she went on to the crux of the matter for virtually all Democrats: the overwhelming need to defeat Donald Trump. In this moment of crisis, Warren said, it is essential “that the next President restores Americans’ faith in good, effective government. . . . We can’t afford to let Donald Trump continue to endanger the lives and livelihoods of every American. And that’s why I’m proud to endorse Joe Biden as President of the United States.”

Given Warren’s rocky history with Biden, which dates back to a 2005 bankruptcy bill that he supported and she vehemently opposed, she could have left things there. (That was pretty much what Sanders did.) Or she could have followed Obama’s example and talked about the future of the Democratic Party. Instead, she went on to recall how, after the Boston Marathon bombing, in 2013, Biden spoke movingly at a memorial service in that city. She also spoke about him swearing her in as a U.S. senator, in 2013, when he jokingly referred to the hell she had given him about the bankruptcy bill but also told her that she would do a great job. “Because that’s the thing about Joe: he wants you in the fight,” she said. “And, when you are in a fight with Joe at your side, you know you have a partner who is committed to getting something good done for this country. Joe Biden is a selfless public servant. He is committed to the fight for social, racial, and economic justice. . . . And now it’s up to all of us to make Joe Biden the next President of the United States.”

How to explain such a warm and fulsome endorsement? Despite their political differences, Warren and Biden have a personal connection based on the fact that “they are both politicians and fighters,” Felicia Wong, the president and C.E.O. of the Roosevelt Institute, an economic-policy think tank that has close ties to Warren, told me on Wednesday afternoon. And, indeed, Biden, in a tweet hailing Warren’s endorsement, said “I’m proud to have the fiercest of fighters, Senator @ewarren, on my side.” Wong also pointed to the fact that Biden, since wrapping up the nomination, has shifted toward Warren on a number of policy issues, including bankruptcy reform. “I think that was super important to her, and he moved on it,” Wong said.

Whatever the circumstances were that led to Warren’s endorsement, her video reminded me of the arguments that a number of commentators have made recently for Biden choosing her as his running mate. As with any veep pick, going with Warren would involve risks and trade-offs, the most obvious of which is that she comes from a part of the country that Biden is virtually sure to carry anyway. But Warren is a national figure rather than a regional one. And, as such, she would bring a number of big advantages to the ticket.

The first, which Ed Kilgore, a Democratic strategist and New York magazine columnist, has emphasized, is that it would help unify Democrats going into the fall. To be sure, the mere presence of Trump on the ballot is already serving as a powerful centripetal force. But the fact remains that the Democratic Party today is a fractious coalition, and much of its progressive wing, which plays a key role in mobilizing support at the local level, has little enthusiasm for Biden. In an interview with Politico on Wednesday, Representative Alexandria Ocasio-Cortez, who supported Sanders during the primary, called on Biden to choose a more progressive running mate who “he knows may push him.” Picking Warren would address this issue, and it would also send a powerful message to the broader American public that, in trying to save the country from Trump, Democrats are willing to overcome their internal rivalries. “Biden-Warren would be an emergency-leadership ticket for perilous times,” Kilgore noted.

It would also elevate a female politician—Biden said last month that he intends to pick a woman—who, during the Democratic primary debates, was consistently the most impressive performer. From early on in the process, Warren’s extensive platform, together with her obvious command of the issues, enabled her largely to dictate the terms of the policy discussion. But she also displayed her toughness and killer instinct. Who could forget the debate in Nevada, on February 20th, when she eviscerated Mike Bloomberg? Warren “would be an effective ‘attack dog’ if needed in the fall,” Mark Green, the veteran New York progressive, pointed out in a Nation article, in which he also argued that Warren had the temperament and experience to “help Biden win and govern.”

Certainly, Warren would be more than able to handle Mike Pence in a Vice-Presidential debate. But Biden could also use her help as he addresses a more immediate challenge that is dominating the news: the policy response to the coronavirus crisis, including the large-scale corporate bailouts that Trump is rolling out. During her time as a politician, Warren has demonstrated a rare ability and eagerness to confront large corporations, big banks, and other powerful financial interests. If Biden had her alongside him, he would instantly become “a power player in the immensely significant decisions that are going to be made in Washington in the coming weeks and months,” Paul Glastris, the editor of The Washington Monthly, wrote a few weeks ago. At the time, Warren had just issued a strict set of conditions to be applied to any bailouts—conditions that other Democrats quickly picked up on. “By choosing Warren as his VP, Biden can put himself in the center of that action and start pushing Trump around on the single biggest issue facing the nation,” Glastris noted. Subsequent proposed bailouts for airlines and other business sectors, the details of which remain pretty murky, have only strengthened his point.

Of course, Biden, as he mulls over his choice, has plenty of other talented female politicians to consider. Among those who have been mentioned are Senator Kamala Harris, of California; Senator Amy Klobuchar, of Minnesota; Senator Tammy Baldwin, of Wisconsin; Senator Catherine Cortez Masto, of Nevada; Governor Gretchen Whitmer, of Michigan; and the former Georgia gubernatorial candidate Stacey Abrams. Substantive arguments can be made for all of these individuals, and no one would envy Biden’s task of reaching a determination. But, on any list of candidates, Warren’s name should surely be very close to the top.