I've always been a fan of teams toying at the end of their roster with hungry, unselfish players that had physical ability. Every once in a while you can get a Dort or Tate or Tucker, etc on a great contract that carves out a well-defined role.
10 day contracts are a great way to encourage hunger and give opportunity to these kind of players.
From a sales/negotiation tactic, if the Cs do like a player, it may make the player a little more desperate to sign a long-term contract, even if the contract has partial guarantees, team options, and its the absolutely minimum the team can offer.
I also think it breathes a little life into the team. Fresh energy can be helpful in those cold February games.