If this conversation were about Mike Conley (who I think is the better player), then I could see the concern. Besides playing time and assets to acquire him, there would also be a significant financial commitment to keep him.
I don't see that issue with Teague. He's a solid guy to fit into the starting job for now, hopefully for a low acquisition cost and his contract isn't egregious. The Jazz don't have to extend him. In fact, I could easily see them flipping him (and possibly Burks) to get an All Star player next year. Both guys are relatively young, but have very good experience.
I think your paranoia is unfounded. It's better to have talent when you can get it. This looks to potentially be one of those opportunities.