But if the CRS needle is set backwards the right/left commands work in reverse, very confusing!
True.
"The LOC needs no course info, it is a pure fly L/R command and does not need heading integration as does the VOR. "
True.
To bring the CRS in line with the published LOC course looks better on the display and aids in position awareness.
Exactly the reason why.
Because the ILS Localizer is a single beam for a given Rwy,
Well, strictly speaking a localiser is actually two beams (or "lobes"). They both are transmitted on the same carrier frequency (108.10 - 111.95) with the left hand lobe modulated at 90Hz and the right hand lobe modulated at 150Hz. Both lobes overlap each other down the extended runway centre line out to around 25 miles. When on centre line the ILS receiver receives equal amounts of 90 and 150Hz signals and your localiser deviation pointer will be centred. If you drift to the left then more 90Hz signal will be received and the ILS receiver will give you a "fly right" signal one your deviation pointer. Drift right and the opposite happens.
Glideslope works in a similar way. i.e two beams but obviously in the vertical plane.