Tie Breaker to reduce orphaned chains? When two different miners find the same block number at roughly the same time, the chain is forked, and there is a bit of a race to develop a longer chain, leaving the alternative orphaned.

Why is there this type of race instead of a tie-breaker among the two competing blocks? 

A simple tie-breaker would be:

"the block with the smaller nonce wins, and the block with the larger nonce should be orphaned immediately".

Does the competition among competing pools offer some advantage I'm not seeing?
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.