Well they won't either. Individual clubs don't have broadcasting rights. Various deals are in place around the world but as far as I know SKY Sports have live broadcast rights for the Carabao Cup. So unless you are playing in the chosen game you won't see it live, maybe the goals later on. What made you think Wigan could decide to show it on a channel of its own?
EFL Championship commentaries on BBC Local radio stations - 7th August 2021 BBC Radio Berkshire - Stoke v Reading BBC Radio Bristol - Bristol City v Blackpool BBC Radio Cambridge - Luton v Peterborough BBC Radio Derby - Derby County v Huddersfield Town BBC Radio Lancashire - Blackburn v Swansea, PNE v Hull City and Bristol City v Blackpool BBC Radio Sheffield - Cardiff v Barnsley and Sheff Utd v Birmingham (evening kick-off) BBC Radio London QPR v Millwall BBC Radio Humberside - match reports from Burnsy every 15mins from Preston North End v Hull City So the other EFL Championship are happy to allow their local BBC radio stations to broadcast commentaries.