The M4 will need to be repaired - GLA or not it will have to be done and if the government steps in to do this then it will step in. Can you imagine what would happen if they let it get to the point it collapsed and killed people ? The properties either side of the M4? Have you heard of CPO's ? they will buy what ever properties they need to buy to do the works.
Removal of the elevated section ? that may well happen aswell - it was built before the M25 and Im sure that the M25 could serve some of the traffic needs. This leaves the section without the A4 underneath this would need to be solved - surface ? whats in the way ?
Its a huge problem
They will not let it get to the state where it becomes a danger to the general public - hence the plans to install netting to catch the bits that are falling off it onto the A4 below. Yes if it gets too bad then it will have to be demolished but we are some way from that happening yet.
On the subject of CPO's the highways agency, central govenment or local councils cannot simply waltz up to somebody and say "here's some money - your home / business is now ours to buldoze". Indeed I beieve anything needing CPOs, especially road schemes has to go to public enquiry - and in this day and age we can all imagine how that would go. It would take years to get through the process and even if it did eventually get aproval the ammount and scale of protests would be imesnse.
As for funding, while any works to the M4 itself would come from the highways Agency (i.e. Central Goverment), the alternative routes (the A40, A30, A4, A316, A312, etc are all funded and maintained by TfL (i.e. the GLA and London's taxpayers). Like I said there is no money or political will to upgrade these alternative routes to acomadate extra traffic if the M4 elevated section had to be closed.