There's only the increase if there's a correlated signal in both channels. Take a contrived example where the left channel is a sine wave and the right channel is the same sine wave phase shifted by 180 degrees. Sum them to mono and you get no signal.
In a more real-world example, suppose you have a stereo track containing something like a string quartet, quite heavily panned. Throwing one side away would be significantly worse than adding a 3dB gain as you'd actually lose information (instruments). The extreme example would be a stereo signal with silence in the left channel and something (anything!) in the right. Collapsing in your way would lead to silence which is obviously incorrect.
That said, the 3dB gain is potentially a problem, so surely the better thing to do would be to add a "hidden" 3dB attenuation when you set the interleave of a genuine stereo track to mono?