Overwatch is currently thriving on three platforms, but 'can we make it four' is the question on everyone's mind. Blizzard has constantly referenced the Switch when asked, to the point where they're kind of tired of it, and slowly but surely they've whittled down their wording to a weaponized response of PR.
When asked by GameSpot about the chances of a Switch or even mobile port, Blizzard producer Matthew Hawley responded: "I think it is one of those things that we constantly evaluate. Where technology is going; where the industry is going. There are challenges in running on the platforms that we're not already on, otherwise we would probably already be on some of those other platforms. We'll see where things go. Certainly, there is a huge number of people out there who have Nintendo Switch and mobile phones, but right now, the core development team is focused on supporting the live game."
Just like Hearthstone -- it's another "we're going to see if the money is there" response. Blizzard doesn't like launching failures, and will go through any lengths to ensure every risk-reward scenario in the book or completely overhaul their games to save them. One day, if the original Overwatch is still around, we could see it. But not anytime soon.