Tie Breaker to reduce orphaned chains?
Consensus rules are often a lot more delicate than they might first appear. Having a tie breaker can actually enable attacks.

If I find a block with a really low nonce, I can gamble to keep it secret and then only when a competing block is found, I can simply neutralize it by broadcasting my low-nonce block. This makes other miners waste their time on a block that will never become part of the chain and it gives me a better chance of finding the next block myself.

I'm not sure if this is true for all possible tie breakers. At least not to the same degree.

The answer by @hedgedandlevered looks at the question from another perspective ("What use would a tie breaker have for the system as a whole?") and is probably generally correct (that is: little to nothing).

However: another example of a tie breaker might be where SegWit signaling blocks are treated preferentially during a tie. That would (assuming support is already > 50%) increase the likelihood of SegWit activating a little as well as providing a slight monetary incentive for (all) miners to activate SegWit. This can be seen as an advantage to the system as a whole and as far as I know does enable attacks by miners in the way the nonce example did.