I believe this is a good time to start using Segwit enabled wallets [...] to make transactions confirm faster.
Transactions will actually not confirm any faster with SegWit. The signature portion of transactions will be discounted by 75%, however all else being equal, a SW transaction with the same discounted fee rate will confirm in the same amount of time a transaction composed with non-SW inputs with the same discounted fee rate.
It is also actually not possible to tell if an address is a SW address until it spends funds, so it would not be possible to force users to use SW addresses.