Totally agree with Alex, above.
There's nothing inherently wrong with headspans as such; after all, they are widely used in other systems in Europe. Cheaper in the short term to erect and less obtrusive visually.
It'd be interesting to see, though, if any studies have been undertaken as to their resilience vs more solid structures. My gut feeling is they are less resilient as they increase the number of variables in the system and are more complex to set up correctly.
Overhead wiring has so many variables:
The interface between train and track, and its relation to the positioning of the OHLE such as cant and the "wobbliness" over junctions
The pan itself
The set-up of the wires - tensioning in particular
The power supply
Human factors - shopping trolleys chucked off bridges, straw blown from agricultural eqpt, etc
Weather - temperature and wind in particular
Headspans probably have an effect on tolerances used and parameters set.
Anyway, Network Ral probably missed a chance when it had all that F&F kit left over from the aborted parts of the GWML electrification - getting rid of it cheaply rather than using many of the parts to replace the remaining headspans out of Padd.
They did re-register some of the crossovers with F+F equipment, although this was exclusively over the Mains. At a crossover structure (and at overlap structures, come to think of it) it's still going to be messy even if everything is already mechanically independent.
At those crossovers, the modus operandi was to "remove on the mains, retain on the reliefs", whereby the existing headspans would have DM/UM registrations removed, but the DR/UR ones would remain. As a result the headspan would still be at risk from the DM/UM, but it was a cost/reliability-on-the-faster-lines tradeoff.
The contractors did remove almost all headspans within stations for NR (AFAIK, one headspan remains within Acton ML, and around 2 or 3 - certainly no more than 5 - remain in West Ealing. (Hanwell looks likely to keep them as it's listed, although if they could provide a sympathetic yet robust headspan design I would love to see it.)
Stations are one of the larger areas of safety risk if a headspan goes down - as you can imagine, "Sudden Unexpected Twenty Five Thousand Volts (Or Whiplash From A Span Wire) While Waiting On A Platform" is probably more of a problem to Joe Public than Joe Public's train being delayed.
That said, re-registering the GWML should be a far less daunting task than other headspan routes, especially as it's the shortest by a long way. Sections have been replaced, and some are in line for being replaced at the moment - there certainly won't be any call for them at Old Oak Common!