More to the point, since I was really talking about through trains from (e.g.) Windsor to Moorgate, are some more items on the LURS site: mainly on "
the Metropolitan in 1906" and "
the last steam train on the underground".
GWR▸ trains did indeed run through from Paddington, and went through Moorgate and on to Aldgate. At the other end they served several places, including Windsor, Richmond, Southall, Maidenhead, Staines and even Reading. And the GER was accessible off the Met, even if the link was only used very briefly. This was of course steam hauled but the Met went all-electric from 1907. I'm not sure how long any electric-hauled service went on.
It's true that initially, when railways were unproved and of uncertain value, they had to fight (and pay) to get into the centre of London. However, it was not long before the streets (and buildings in between) were being torn up or down to put in railways. More could have been done to link them to commuter lines at termini, if it had looked profitable. However, while railway companies did cooperate (and merge) when it suited them, their objectives often didn't align. Or their egos, in some cases.
So I still think it is a puzzle - why were this "proto-Crossrail" and Snow Hill not used a lot more in the 40 years or so of steam traction? Turning steam trains in cramped stations like Aldgate can't have been easy. Post 1900 the conversion of the underground (SSR) lines to electric would have - did - lead to their taking over the surface lines to run on, rather than vice versa.