No? What makes you think so?

Then what do you mean, some applications organize hot and cold data in RAM and storage respectively? Just about every application does it.

A silly but realistic example: lots of applications leak a bit of memory here and there.

Almost by definition, that leaked memory is never accessed again, so it's very cold. But the applications don't put this on disk by themselves. (If the app's developers knew about which specific bit is leaking, they'd rather fix the leak then write it to disk.)

That's just recognizing that there's a spectrum of hotness to data. But the question remains: if all the data that the application wants to keep in memory does fit in memory, why do you need swap?