The payment word has a history involving inherited land and offices.
The French-derived feudal sense of fee named an estate. It extended to inheritable offices of service, and payment associated with those offices helped lead to the broader service-charge sense.
Sources
- Merriam-Webster: fee
The entry documents the feudal estate and service-charge senses and the Anglo-French fé/fief route.
- Etymonline: fee
The entry describes extension from feudal landholdings to inheritable offices, then remuneration for office and work.