Nice idea, but I think it would also have required late C20th/C21st patterns of commuting to make it work. Beyond Aylesbury/Oxford was really not London commuterbelt in the 60s, or even in the 80s, it took the M40 (among other things) to change that.
What would have been the point? The section from Rugby to Aylesbury went through open countryside, and only one small town (Brackley). Nottingham/Loughborough/Leicester/Rugby to London were all catered for by alternative routes with plenty of capacity on them in the mid-sixties. Nottingham-Oxford (and beyond) could have been served Nottingham-Loughborough-Leicester-Market Harborough-Northampton-Bletchley -Oxford, serving Northampton (a much bigger town than Rugby) and still close the GC main line over its entire length. But only one daytime GC train used the Woodford-Banbury link, so clearly not much traffic in '66