BA signing a franchise deal means licensing their brand to another company and giving them limited freedom to use that brand to sell a product or service.
By necessity, the act of brand licencing means BA would give up some meaningful degree of control of their brand. The question is how the franchise royalty stacks up against the change in perceived value of the BA brand.
How willing would BA be to see their logo advertising flights to Southend ? SEN is a nice airport (been through twice) but it still has a bit of a LCC feel that might not gel with BA's 'To fly to serve' marketing approach. On the same theme, before BA offloaded regional ops to Flybe, the presence of BA at Luton for example felt (to me at least) somewhat odd