I actually don't hate the idea. I wouldn't do the proposed trade, but it is an interesting idea to start from. My counter-proposal would be:
Booker, Burke, and our other non-guaranteed contracts for Dwill and Plumlee. Then we pick Kaminsky at #12.
I would stick with the starting lineup that helped us become a top team after the All-Star break and add an upgraded bench. Dwill, Burks, Kaminsky, and Plumlee would be a major upgrade over Burke, Ingles, Milsap, and Booker. That is a very solid 9 man rotation - one I'd definitely take over our current one. And his contract would expire before anyone is due an extension, so we wouldn't risk losing Gobert because of DWill's contract.
The main point I'd like to make with this trade is everyone is talking about the Golden State model lately. They drafted Curry, Thompson, Green, and Barnes. They traded for Bogut. Then they were able to trade for IGGY. They built mostly from the ground up and traded for complimentary pieces. Remember, Andre Iguodala had a rough few years and was on the "back-nine" of his career as well. GS still traded for him and his "bloated contract" and got a player that struggled much of his time. He was a former all-star that wasn't playing up to his contract and struggled off the bench. Then he re-appears in the Finals, wins Finals MVP, and is the main reason his team won the Finals. It looked like GS made a horrible decision to give up 2 unprotected 1sts to the Jazz so they could have the cap space to make the trade - then he wins them a championship and people think DL should get a ring for facilitating that trade. Iggy averaged 8 PPG, 3 APG, and 3 RPG on the season, BUT he showed up on the big stage and helped them win a championship.
Iggy, Lee, and Bogut all are on bad contracts, BUT they had Green, Barnes, and Thompson all on rookie deals so it didn't kill them. The Jazz are in a similar position. Gobert, Hood, Exum, Plumlee, and Kaminsky (or whoever we pick at #12) would all still be on their rookie deals for the entirety of DWill's contract and the 9-man rotation of Gobert, Favors, Hayward, Hood, Exum, Dwill, Burks, Kaminsky, and Plumlee would have 2 full years together. If there is ever a time to make a trade like this, NOW IS THE TIME!