Consider a very old wood floor. What are the reasons beyond purely aesthetic to sand and finish it? In particular, does finish fills the small gaps between the wood pieces, thus isolating better the room?
Although finish treatment of old wood flooring might (to some small degree) fill small gaps between planks, this is not the primary purpose (nor will it do that very well).
As you suspect, the primary benefits are aesthetics and protection. As an added benefit, a finished wood floor is also easier to keep clean.