<<<Do you think it would be possible to do this automatically?>>>
Probably not, but you might take a shot at Steve's Noise Gate...download/file.php?id=1272
The premise is pretty simple. All sounds below a certain volume are reduced or deleted.
"Echo Reduction" in this case (and most cases) wouldn't work because the echo is not a perfect version of the original voice. It's the voice having gone through at least two A/D conversions and the tinny, strained sound of computer speakers bounced against the bedroom walls.
The system sees it as two different performers that sound a little like each other.
Noise reduction works in a similar way. The definition of "noise" is strict and anything that isn't "noise" becomes a performer in the show.