I feel like if Twitter fact-checked one tweet from a high-profile Democrat for every one they did of a high-profile Republican, there would be a lot less outcry over the situation. I know the president happens to be a high-profile Republican, and as a result he's a more salient target for fact-checking, but lying and being wrong are both bipartisan strategies. The accusation is that Twitter is almost completely staffed by Dem voters and that they're biased as a result. Everyone knows the premise of that accusation is true, so a little formal knod to dispel the conclusion would be welcome.
My emotion-driven reaction here (“ha! They’d run out of lies from side A before scratching the surface with side B!”) is _exactly_ why trying something like this would be a good move.