As you say, there would be massive institutional resistance to blanket Class E from all sides, and you've already identified the reason - if you have mandatory ATC for all IFR traffic throughout the entire FIR, 24/7, then you need ATCOs to control it.
Who pays for them? The GA sector isn't interested, they are quite happy as they are in Class G and will point to the complete absence of collisions in IMC in Class G since (probably?) WW2. The airlines via increased route charges? Fat chance. NATS? What's in it for them as a profit-making, private company? The taxpayer via the CAA/military? Not a snowballs chance in the current climate, at least not until there is a problem that needs addressing because the public becomes interested in it - ie. multiple collisions between uncontrolled traffic in IMC.