Yeah, Bath is a bit of a special case obviously, with the whole city covered by World Heritage Status, and UNESCO have made multiple threats to remove that status in recent years over new developments, so the council is a lot more sensitive to anything that could possibly threaten that.
As I understand it the council just want to see proof that there would be a noticeable benefit to Bath from the wiring, and to be honest I agree with them. Wiring through Bath is an eyesore, the railway runs above the city and any wiring, even sensitively done, will threaten that. I used to live further East and watched the eyesore bombproof GWML wiring significant alter the Thames Valley. As it stands wiring alone will just shave a minute or two off the journey times from London to Bristol, if that because even as it is the IETs have a tendency to catch up to the preceding local service by Bathampton Junction. To allow it they would want either:
A commitment to improve services through Bath, through delivery of MetroWest and provision of enough Bi-Mode units. As it stands the local service in Bath is a joke, the stoppers are overcrowded, infrequent and short formed, the IETs save the service to Bristol, but if there's a problem in London they can disappear. Bi modes are wanted because otherwise the benefit of electrification is even more minimal, the 166s and 158s create the majority of pollution from trains, and would otherwise still run on Diesel under the wires. Investment in the West has been very minimal, and the attitude has always been we get the leftovers from London, without improved local services this would further that, basically just decreasing journey times for those on long distance trains from London
I also understand they wouldn't stand in the way of it if the majority of the trains to run through Bath after were electric only (i.e. majority corverted 80X's or 387s, not just 1 387 a day like Cardiff.)