The same people who would oppose a new right of way would oppose both a six month closure and the demolition of so many historic (albeit very unexceptional 150 years ago) overbridges.The only practical alternative for Crewe-Chester electrification to building a new line would be to close the line for six months or more so that the bridges can be replaced without having to take precauations like those taken for working on railway lines.
Temporary road surfaces across the trackbeds and such things.
But I doubt a six month closure would go down well. ...
Some people dedicate their lives to opposing anything that benefits others but not themselves.
One has to not lose sight that this is a realatively inexpensive place to build a new line with modern features and a difficult and expensive existing line to upgrade that wouldn't be all that wonderful in the end. The gut reaction that it is cheaper to upgrade than replace applies less here. It might be a little cheaper to buy something that is vastly inferior. Turning back HS-captive trains at Chester (or even Hooton or Birkenhead) when HS2 finally reaches Phase 2 is a possibility. Meanwhile it is a good place to do a pilot HS construction (and operation) which can afford to learn by making inevitable minor mistakes (unlike OOC which cannot).
And yes, Chester station could be expanded to the North, and Crewe station expanded to the West with incompatible platforms.