An All Line Rover doesn't have a cross-London marker and specifically excludes travel across London by underground.
Sorry, I didn't mean to imply that it was valid .... I should have said that "a different one-time National Rail ticket for the same journey today would include the Underground sector because it would have a Maltese Cross" but even the National Rail ticket has the break of journey issue in future, that's to say that today it'd be valid to Bond Street, say, on the Underground but not to recommence the journey from there whereas with Crossrail/Elizabeth line it should be valid for break of journey.
The core isn't part of the national rail network anymore than the Heathrow spur is part of the national rail network.
But Heathrow is explicitly excluded from the all-line rover ticket, although it's valid for one journey with a Britrail ticket I recall, given that I used it when I had a Britrail ticket quite some time ago ......
EDIT and I meant to go on and say .... Crossrail/Elizabeth Line
could be excluded from the all-line rover also, but then you'd have a single train on which the ticket was valid into London on one side and out of London on the other but not for the bit in the middle, which would be confusing and perhaps a bit silly.
And finally .... this isn't an academic question from me because I'm likely to be using an all-line rover in the near future, I'd planned to do so in October with my new Senior Railcard but I've put off my plans for a little while now, and there's always the chance that Crossrail and even Bond Street will be open by the time I do!