Not a bad idea.
The appearance is Axelrod-designed posturing to reach out to independents via signalling , but still, the results might be healthy in a minor way. Decades of gerrymandering has created so many “safe” districts that the House has become far more polarized in political terms than the voting public as Congressmen increasingly represent only their party’s activist base – and sometimes only the extreme edge of that. Then the majoritarian rules of the House aggravate partisan feelings of people already inclined to lack goodwill towards one another.
The POTUS for his part lives in a rarefied bubble that cuts him off from the public and shields him from disagreement or politically unwelcome points of view. Going in to the lion’s den from time to time keeps the wits sharp and brings a wider range of voices into the debate.