In the end a sponsor for a Ground will look at long term opportunity for exposure. Number of hits. You mention Global Brand - well if a business wants a global price it has to have Global exposure. Rugby does not have that in the same way as football. There is some exposure in Japan but other far east markets there is not and even there it is very minority.
It is in the main a limited colonial sport with no global appeal. Football has. So in negotiations the association with the football club becomes a consideration as even at League One level it attracts the same exposure level as Wasps and Wasps are at the pinnacle of their game So yes it annoys them like hell.
Shirt sponsorship is small beer