O&W transactions will always cost more than regular BCH transactions (much like how memo txs will always cost more than normal BCH txs), so not sure how that would be the case
Don't know enough about omni to comment specifically, but if, for example, omni tx is much faster than crippled BCH, then, onmi wins.
Omni txs are BCH txs, just with some extra OP_RETURN data attached (same with memo). The post you just made is a BCH tx. You can't cripple BCH without also crippling memo and omni.
It helps BCH by increasing the number of BCH txs. More txs = more fees for miners = more security for everyone. And burning makes everyone else's BCH more rare and thus more valuable.