I agree that some properties could be rebranded, but the brand affiliation of many FS and Fairmont properties is very strong. I´m not convinced merging the brands would make a huge amount of sense. However, many Swissotel properties are somewhat generic properties that could be affiliated with any 3.5*-4* chain.

The status of "By Invitation" is somewhat ambigious, see this thread. In any case I wouldn´t call it a true loyalty program - more of an unofficial guest recognition program without any published qualifying criteria and somewhat vague benefits.