Why were railways grouped into four roughly geographical companies back in 1923 ?
Would this not work better today instead of the franchise system ?
There were several different models for grouping.
I wouldn't really call what happened more than vaguely geographic.
It was mostly based on the railways which already had close working relationships (eg GN, NER and NB for LNER, and LNWR, Midland and Caledonian for LMS).
The idea was also to retain significant competition on the main flows to London (eg from Scotland, Manchester, Leeds, Birmingham).
But some railways were very hard to place (eg GC, Cambrian) and it was largely pot luck where they ended up.
The LMS was eventually considered "too big", so the GC went to the LNER and the Cambrian to the GWR.
The LMS and LNER intertwined in the east midlands and west/south Yorkshire and through Scotland, and so did GWR and Southern in the west country.
LMS penetrated far into GWR-land at Bristol and Swansea. In return GWR reached Chester, and the LNER reached Wrexham and Stafford.
The LMS reached Goole and Shoeburyness.
BR eventually imposed geographic Regional boundaries after nationalisation (but it took them until 1963, and threw up many operating anomalies).
BR's sectors then unpicked all that in the 1980s, creating Intercity, NSE and RR, across Regional boundaries.
Privatisation then split the sectors into smaller pieces and franchised them out separately.
Meanwhile Railtrack/Network Rail has struggled with its structure since being separated from BR in 1993.
It currently has 9 Routes, some of which do not map well onto the franchises.
There are now trends to integrate franchises with NR routes (LNER being one), but it is a slow process.
Freight and franchises like XC, TPE and Thameslink will cross any geographic boundary you draw.
And where will HS1 and HS2 fit (not NR lines)?