AFAIK the intent of segwit is not to reduce overhead but to fix tx malleability. As an consequence of the politicized block size debate a discount was added to increase the number of txs per block--and this was seen as a compromise for the big blocker camp. It turns out you can roll it out with a softfork as well (and provide script versioning), making it a safer alternative to upping the limit with a contentious hardfork.

Can you clarify what you mean by the majority hash rate needs to enforce the new rules?