I bet some companies are looking into it, you might see one used in coming next generation ASICs
No you wont.
Mining is simply: generate a header, then run the nonce from 0 to 2^32-1
Changing that nonce order will have no effect at all on luck - zero - none - absolutely no reason to do it.
You also cannot selectively choose nonces that will give better results - since you have to hash the nonce to find out - which is what a miner does.
Anything more complicated than simply incrementing the nonce would slow down mining, and decrease efficiency. Each chip is changing the nonce around 500
billion times a second. There is no time to mess around -- especially when, as Kano says, there is no benefit.
(Modern ASICs also roll bits in other fields, but same idea)