I think that the idea would be for passengers from Colne inwards would require to change at Rose Grove rather than to incur the infrastructural and signalling costs of a chord of the type and route you so describe.
Look at the associated costs incurred in the Todmorden Chord as a benchmark.
Yes, quite right - or reversal perhaps? So Colne, Nelson, Brierfield, Burnley (Bank Top), Burnley (Barracks), Rosegrove, Burnley (Manchester Road), Towneley (let's not forget dear old Towneley - lots of population there), Todmorden, Walsden etc. etc. and Manchester!
I know Burnley (well I did, lived there as a lad, 1947 to 1966 but it's changed a lot) and I observe that the railways are higher up than is the town. Back in the 50s my Dad and I speculated on the possibility of the eastern chord, we had it leaving the Colne line at about Reedley Halt (Barden Lane), swinging south on the contour, crossing behind Bank Hall Pit (about a mile north of Turf Moor), passing behind The Ridge (and Brunshaw housing area) hugging the opposite side of the valley to the Yorkshire Line, until finally crossing over and joining up to the Copy Pit line around Cliviger (not far short of Holme Tunnel, in fact). A nice thought experiment, and in engineering terms do-able, but not just to connect a dead-end branch, as it is now. (In those days the Colne "Branch" was the Main Line and it went on to Skipton, our experiment made more sense then).