Not true for a lot of (widely used) systems. Both the NY subway and London Underground are manually driven for the majority of lines.
Paris has the same, and also a number of lines (1, 4, 14, and soon 15) which have no driver at all.
NYC Subway is an outlier in how obsolete everything is.
Grand Paris Express' president also talked about this, and compared the 2nd avenue subway to the Grand Paris Express (well, one cost $4.45 billion for 1.8 mi / 2.9 km and 4 stations; the first line of GPE, 15 south is 33km, 16 stations, and costs ~8 billion euros so it's a really bad comparison), and has said that if he had to do things the way the MTA do it, GPE would have gone nowhere.
Barcelona, on the other hand, would qualify for everything except line 4.
Also if we want to quibble, at least a few sections of the Bakerloo and Piccadilly lines (which are still completely manually driven) were opened after 1906.
From 1907 onwards every newly built line was automated from opening (though indeed extensions or "new" lines made by splitting an existing line were sometimes manually driven).
(The Jubilee line in 1979 – which started out being manually driven – wouldn't count according to your criteria, because part of it was "made by splitting an existing line", and apart from being heavy rail, arguably Crossrail could be argued to be an extension, too, even though it does operate automatically on the new-built bits, i.e. the central section plus the Abbey Wood branch.)