It would be strange were you not to find other boat remains in mountains from the flood. Many nations retain stories of Noah and the ark; Greco-Roman and Chinese literature describe handfuls of people and animals surviving here and there on high places or anything which could float for most of a year. The story of Noah is true; the idea that nothing survived outside of the ark is problematical.
The multiplicity of flood stories is more likely the result of a single shared memory stemming from the retelling of the original flood story by Grandpa Noah, propagating into future generations tracking on migration paths.
Therefore, no, nothing about the event predicts finding multiple boats lying around. Quite the opposite. If the story is true, as you seem to grant (and I agree), then the supernatural design of the event must be considered. If, as the story infers, God intended to wipe out all human and otherwise mammalian life, and only spare Noah et al, and if only Noah acted on the belief that a crisis was impending, then it follows that God, as God, would be able to accomplish his stated goal, and that Noah would therefore be the only one prepared for the massive scale of the approaching cataclysm.