If only they came with labels. Unfortunately, the hallmark of a web-based April Fool story is that it comes clothed as a real story. They're deliberately crafted to sucker you in and convince you to read two to six paragraphs before you figure out that they're made of lies.
In other words, April Fool's Day is a linkbait competition. I think that's why it has worn out its welcome for so many people. Linkbait used to be more funny when it was rare. Now it's like celebrating Mosquito Day, or Spam Email Day.
Yours would be a reasonable suggestion if every April Fool story was submitted with a prominent label reading [APRIL FOOL]. But that would spoil the fun, wouldn't it? If there's anything less fun than an April Fool story, it's an inartful April Fool story.
Frankly I think Google raised the bar years ago when they announced Gmail on April 1. I no longer think an April Fool story is any good unless it (a) sounds like an obvious April Fool joke but (b) is 100% true.