This is a rare lame argument you're making. WSJ passed on the story because it didn't have any sort of basis. That's what happened. After it broke, the WSJ covered the story in the sense that they recognized it existed, and then also opined about it. So what? So did
the NY Times. And
WaPo. So did
CNN and
CNN. And pretty much everyone else.
The reason responsible media - both right- and left-leaning - acted cautiously on the story was that they couldn't find much of a basis for it. Joints like the NY Post don't care much about that.
Don't get me wrong, the broader point you brought up to begin with - that the media by and large actively wanted Biden to win and didn't want to do anything to jeopardize that - is probably true. Especially after what happened with Comey and Clinton, they were probably especially nervous about reporting anything that wasn't rock solid that might inadvertently help Trump. But the strange tack you're following now, trying to differentiate between the WSJ and more left-leaning MSM outlets, just doesn't pass the smell test.