It looks good on paper but in practice it probably wouldn’t work.
For starters TfL has no money and what with everything going on in terms of Covid-19 and Lockdown I can’t see the Overground expanding for the foreseeable future - if ever at this rate! A lot of things will be delayed if not postponed.
A lot of the metro routes intersect with outer surburban services in SE London as well, hence why the Gillingham via Woolwich service was binned off to Thameslink because it was partly to separate the outer suburban routes from the metro inners in the event of a TfL takeover however according this proposal it would involve an awful lot of services terminating at Dartford, which will still leave the Gravesend service with SouthEastern by the looks of things.
Another thing is that large parts of South and South East London stations have access to at least two London terminals, usually a West End terminal and a City terminal, and it’s three terminals if your on the Bexleyheath and Woolwich lines, the only exceptions to this is the Penge East line which only has Victoria (with peaks to and from Blackfriars but that doesn’t count) TfL’s idea was to have “one line one terminal” and this did not go down too well with commuters who have been used to having two or three options.
A part of me wishes TfL could takeover suburban services but I don’t think slapping the TfL roundel on trains is going to solve anything, in fact by the looks of the plans it looks downright confusing.
Thanks for posting the videos though.