A trial could actually have a huge impact on US politics. The bipartisan consensus is that you don't go after your political enemies in court. Democrats never touched Bush or put Trump on actual trial, after all. Even Nixon was left alone after he resigned.

This is necessary for the function of the US state. The president needs to be able to break the law without worrying about personal consequences so he can control the proles and build empire and stomp down on the left flank, all without ever being subject to any personal inconvenience.

Putting Obama on trial might be the beginning of an actual partisan split. Democrats could stop thinking of Republicans as colleagues and start thinking of them as enemies, especially if the trial actually results in real material harm to Obama.

... or nothing ever happens and it'll be a friendly kayfabe show trial that everyone benefits from, and the bipartisan consensus will hold.