Reason 1: The "network" version's usual broadcast area also covers the Isle of Man and the Channel Islands, which are not part of England.
Reason 2: The "network" version is also the default UK sustaining feed if any/all of the Devolved Nations' own variants fall off air.
I think these are both pretty much the reason default BBC is not called BBC England. Also, there's no England programming. It's either regional or, the vast majority of the time, generic UK programming; even if Scotland, Wales & Northern Ireland happen to opt out from the network all at once. There's no Reporting England, no politics show called St Georges Eye, no soap opera that's 'English', akin to River City ( I don't understand why it's Scotland only anyhow).
Like I touched upon earlier, the British establishment don't see England as any sort of actual entity. They see it as default Britain, whilst Scotland, Wales & North Ireland are 'exotic' Britain. This is why it's not seen as an anomoly to most of the suits in Whitehall that Westminster continues to control almost every aspect of life in England whilst much is devolved in the 'nations'. The idea of England is an oxymoron to them. Something like an English Parliament, to them, would be like France giving Corsica a devolved parliament then having to give mainland France a parliament. They view it a lot like China in a way. Scotland, Wales & Northern Ireland are special administrative areas, like Hong Kong and Macau with their own local regimes, whereas England is mainland China, mostly controlled from the centre. China's provinces. Guangdong, Hubei, Quinghai etc can be substituted for North West, East Midlands, South West etc. It's ignorant towards England and patronising towards Scotland, Wales & Northern Ireland and causes issues within the UK that I believe have always been avoidable (accepting that Northern Ireland has a somewhat complicated situation). But hey, these suits also think Liverpool is a large, rundown housing estate on the outskirts of Manchester, rather than an entirely separate city of similar stature. That's what we're up against in this country.