Hashing process could be optimized by mining for blocks with only one constant coinbase transaction - so no other transactions will fit in the block. BIP 0034 prevents it.
No, BIP 34 prevents duplicate transactions because they were an ugly corner case.
It was heavily discussed, so searching these forums for it will provide enlightenment on the matter. The short version is that allowing duplicate generate transactions was surprising, but realizing that they could be spent and then mined again was even more surprising. In theory, whole strings of transactions with identical IDs could be made that way.
That's a part of Bitcoin history I've missed
Looks like easier mining of empty blocks with duplicate coinbase transactions was not considered as a possible attack, but developers sticked to their clever hack of using transaction hash as an key. Anyway, the mining advantage would be small, something like 2% and this vulnerability was fixed without being discovered 
