Historically, US presidents go silent on purely political topics. The idea is to avoid conflicts of interest like a general who takes orders from former Pres., rather than current. Also avoids the problem on internet stage of “who is speaking for the US?”
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Of course those norms were defied by Trump but as usual with Democrats that are playing by a rule book that has been burned.
Because historically, left or right, most presidents have cared about peaceful transition of power and have understood the negative consequences of a former president taking a public position.
Hopefully that helps answer the question