The "M" in the original "LMS" referred to the Midland Railway, which is really what EMR is (ignoring the XC dimension of the Midland which is always overlooked).
LNWR, although seemingly purloined by WMT as its brand, is much more "heritage" than LMS for West Coast services.
It was the largest joint-stock company in the country at grouping in 1923 (as was its successor the LMS).
The proposed DfT's "LMS" is also a pale shadow of the real LMS which reached Southend, Swansea, Leeds, Goole, Aberdeen, Wick and Kyle of Lochalsh.