Dollars to donuts he's a reliever long term. That doesn't mean that he doesn't get anything out of starting now. He learns how to deal with different game scenarios, how to pace himself, how to reach back for extra velocity when he needs to. In short, there's no downside to him for starting this year.
The only possible downside is whether he's blocking another starting prospect, but I'd have Barnes on the chopping block before Jax anyway, so I doubt it. I say give him the rest of the year as a starter with an eye to a relief role in 2022.