Unfortunately, iOS doesn't allow background actions except for a very limited number of cases, so you'll have to have Keychain opened to sign transactions.
I wonder what is the reason behind that. Security?
I am honestly asking. I have not used iOS so far, and probably I will not use it in the future either. The iPhones and the Apple products in general are much more expensive than the Android smartphones.
Having too many Apps in background could impact battery and performance, so I understand that they impose limitations. Although it should be up to users to be able to authorize this kind of behavior. They render some features impossible but Apple doesn't care.