In that link there is a description how to use phase correlation to figure a global shift-translation between two frames. GLOBAL. One vector for the whole image. Like when a camera is panning across a still scene.
Again: You DON'T track several individual objects within one frame via phase correlation. The frame as a whole, yes. But not individual objects within. For such a thing, you would need to split the frame in smaller sections, and then compare different sections against each other, and so on. Which in turn leads you, ad ultimo, to a blockbased motion search scheme. Tadaa.
Long story short: blockbased motion search has been invented because phase correlation is not (or not-very-well) suited to find local motion of individual objects.
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It wouldn't be a problem if my eyes didn't clearly tell me that small difference is a motion and not just noise.
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Yes, of course! I'm fully with you here!
It's just that exactly THAT is THE problem in denoising:
"Hey, look at that, it is blataneously obvious that
{this} is an object and
{that} is just noise! Isn't it! Why can't the darn algorithm see that, too?"
That ever was, ever is, and will keep to be, the problem.