I don't think anyone is jumping up and down for joy that Turner is a Cub now. I don't think anyone here would have crafted an offseason plan that would have included Turner. He's getting paid more than he's likely worth.
But, given where this offseason has led the Cubs brass, he's a decent signing this late in the ballgame. While I do agree it's important to consider cap space on any signings, I don't see how overpaying for a bench bat when there is plenty in the coffers to not only sign Turner and possibly another pitcher, but they'd still have plenty left at the trade deadline. Overspending on a budget actually works if you managed to keep enough in reserve to be able to make those types of signings.
I also think he'll end up with a lot of at bats, and not necessarily at the expense of the better bats. Injuries happen, and Turner is 100% the first DH option the moment someone is missing time, whether it's for a DL stint or days of rest. I think there will be a lot of rotating of outfielders to get Suzuki plenty of time in the field since he's not all that keen on being a full time DH.
Grichuk just wasn't coming to Chicago. There is already 4 OFers blocking him from playing the field, and there is really no position he fills as a bench guy that wasn't already covered. Grichuck hasn't played a single inning at 1b in his entire MLB career, and that's something that was a bit needed. As much as Ryanrc thinks any athlete can play 1b, and in a pinch, I think good athletes can catch a ball, I have to agree with Cubs brass that having one with experience that can also hit is a much better idea than just winging it.
Whether Turner deserves 6m or not:
A combination of Workman, Brujan, Kelly, Berti and Canario is not as good of a bench as Workman, Turner, Kelly, Berti and Canario, and benches do matter. It drove me nuts seeing Wisdom being the best bench bat at times in previous seasons. No one is going to be sitting here waiting for "I told you so's" at the end of the season if the Cubs stay relatively healthy all year and Turner only logs about 125-150 at bats. You sign a decent bench bat for the risk there will be that many and possibly a whole lot more.