... I've never once heard anyone refer to the DLR, Trams or Cable Car as the tube and I only ever hear BBC London annoyingly refer to LO as the tube but no one else. The problem with the clutter argument is that as soon as TfL gets its hands on NR routes, it puts it on the tube map - leading to the cluttered mess it is now and will no doubt continue doing it. Thameslink is one of the busiest lines in the country and is left off because they don't run it while the 4tph Enfield & Cheshunt line is on there. That isn't putting the interests of passengers first. Furthermore, to find a printed copy of the Rail & Tube map to take with you at a TfL station is like gold dust - even at stations which are also served by other TOCs, they only push the tube map which for my station doesn't show half of the services. TfL claims they want an integrated transport network in London but they are purposely not trying to integrate non-TfL NR lines and pretending the only way to do it is by devolution. The West Midlands has proven an integrated transport network does not need to be run by one operator.
Additions to the TfL tube map are where those lines are completely under TfL's control to the limit of services, e.g. the most far-flung lines such as Shenfield, Cheshunt, Watford Junction, and Amersham/Chesham (historic) are well outside TfL's primary brief which only covers the GLA. When Crossrail opens fully, the line to Reading will probably be added as would the Hayes branch if it gets a Bakerloo service.
To add the Thameslink core would be confusing as that splits both north of St Pancras and South of Blackfriars. So do they also include London Bridge? Then why not Elephant and Castle, - or might as well go to East Croydon. Then in the north there's Finsbury Park & West Hampstead. If that's done they might as well add Stratford to Tottenham Hale, Stratford International to St Pancras, London Bridge to Lewisham and Abbey Wood, Waterloo to Richmond & Wimbledon, and Victoria to Balham (National Rail). Once the map is extended beyond TfL's rail services there would be constant pleading of cases for any of these.
It's true that Thameslink is one of the busiest lines in the country but most of that is into the core from outside (and vice versa), principally commuter traffic with a reduced flow off-peak. So most of those passengers either know central London rail services like the back of their hand or have already accessed the information at their stations of origin (NR). Despite that, I've not noticed the lack of the TfL & National Rail maps, especially in Zone 1.