That is good and some gateways do this as well but many don't and, having the tokens under your control means you don't have to co-ordinate a transfer between 2

That is good and some gateways do this as well but many don't and, having the tokens under your control means you don't have to co-ordinate a transfer between 2 other parties, but just proxy a new outbound request to your new provider and be done with it.