Coinbase and Bitstamp next?
I don't use Coinbase so can't confirm, but according to
https://en.bitcoin.it/wiki/Bech32_adoption they already support withdrawals to native SegWit addresses.
Firstly because it's not them who pay the fees, but us, the users.
True, but I doubt very much exchanges which do start supporting SegWit will reduce their fees in turn. More likely they will continue to charge overpriced fees (which will be even more overpriced once they've switched from Legacy to SegWit) and will just pocket the difference.