The problem with the Underground map is that it has gradually become more complex as new things have been added to it over the years. There've been new lines, fare zones, accessibility information, the Overground network, out-of-station interchanges, etc. All this is interesting to enthusiasts and to some London residents. It becomes pretty daunting to someone who just wants to plan a journey. I should think it's now impossible to design an up-to-date version without some major compromises. Before any new design is attempted there would need to be agreement about the principal objectives. Then various drafts could be constructed to achieve those objectives and evaluate how acceptable or otherwise the compromises might be.
Yes, the way all sort of things have been added to the Tube (Underground) map is what has spoilt it, especially as most peoples is exposure to it is in the small folded version, which has ended with far to much being squeezed on to it, resulting in rather a mess; while at the same time not everything, so its incomplete...
So for the Tube, a complete redesign, with just the Tube - the Overground, DLR, Tramlink all have their own maps, the Tube should be the same.
And to go with it, an overall London 'rail map', with all the rail services, both TfL (EL, Tube, Overground, DLR, Tramlink) and NR (GBR to be) - perhaps in three versions, for 'central London' (to cover Zones 1-3?), 'Greater London' (Zones 1-6, perhaps a bit more - but not much!), and a 'London and Hinterland' (at least the former LT area, probably out to cover all the 'Project Oval' territory). And with the development'Bakerloop', 'Superloop', and similar express bus services, there is perhaps a case for carefully considering whether these should be included ... I'm rather in two minds on this. But alongside the 'Rail' map, there is a need for a 'Bus' map (which should also show rail lines, if only in outline).