I don't really believe they'd buy Brodie out, but I do think they'd be willing to trade him. Especially since Toronto has stated they will be looking to reshape their defense.
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If Washington decides to try to be competitive next year then I think he'd be a good fit in DC and unlike Hanifin who in my eyes is quite overrated, Brodie is likely going to be a bit undervalued because he wasn't great this last postseason. He isn't showing any signs of slowing down either:
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(Look at that, another defenseman who was immediately at or near his peak when he entered the league in his early 20s!)
Of course if Washington decides to be less aggressive and to use next year as more of a development year for their prospects I don't think the fit is as strong because I don't see him really being more than a rental.