Stop. Paying. So. Much. Attention. To. Batting. Average.It.Is.Not.A.Good.Statistic.
Let's just start off all agreeing that a walk gets you the same result as a single. Right? Right? So if getting a single is good because it raises your batting average, then getting a walk should also be good, even though it doesn't raise your batting average. Agree?
This is why nobody in baseball front offices cares about batting average any more. Read or watch Moneyball, and you'll be caught up to the major innovation of 2002 - on base percentage. A lot of better tools available these days, but baby steps.
Noot has a .355 OBP. He's at 121 OPS+, 117 wRC+ for the season. He is clearly an above average player who has trouble staying healthy. And everyone in the league knows his health history so odds are you aren't going to get a ton of value for him in a trade. If you can get good value, obviously go for it. But scrapping him for parts because of his batting average is not it.