Regardless of the technical and economic merits of wires vs big batteries vs smaller batteries and ultra-rapid charging, I think funding is a big issue.
If a bus operator wants (or is required) to get battery electric buses, then that's likely their investment/lease cost (paid from farebox & subsidy)
Charging infrastructure provision is private sector too.
However trams/trolleybus wiring would almost certainly be a public sector project, so expect a painful process of endless business cases and studies, then get the money out of some central government scheme. Whitehall now decides whether individual local authorities can build public toilets (see link below), I don't think they're going to make it easy to get hundreds of millions in funding for trolleybus/trams, especially when project delivery has been patchy.
The prospectus for the second round of the £30 million Changing Places toilets programme.
www.gov.uk