I actually really like the idea of Dolby Pro Logic II being the default mixdown in handbrake, it is very cool technology, and widely compatible since it is stored as stereo.

But handbrake uses the popular and bad implementation which has no 90deg phase shift. The audio may be unbalanced left-to-right in the mixdown if the surround channels are highly correlated. The only free program I have ever found that actually implements a proper 90deg shift for its downmixing is QAAC. I have done some tests manually splitting the audio out, sending it through QAAC, and muxing it back with the video, and the results are very good!

All that would need to be done to make this option great is for handbrake to rotate the rear channels' phase 90deg before putting them in the downmix matrix. This can be achieved with convolution, creating a Hilbert transform (the way I assume QAAC does it).

Is there any interest in this? Due to the unbalance issues, I find the "Dolby Pro Logic II" option unusable, but I would personally use it all the time if they implemented it properly.

BTW, this is the downmixing matrix I used in QAAC if anyone wants to try this out. The j represents a 90deg phase shift.
1 0 0.7071067811865476 0 -0.8660254037844386j -0.5j
0 1 0.7071067811865476 0 0.5j 0.8660254037844386j