I agree, I know why the Coyotes did this deal, but if you have a 1C, you have to find room for him some how. Maybe, they feel they have someone they can promote to take Stepans place.
The Rangers traded Stepan for a variety of reasons but ultimately yeah it does hurt them down the middle for sure.
One reason is it's possible they think that Zibanejad can take over as their true 1C. It's a gamble but he's young and has a higher offensive potential than Stepan. Really unfortunate he broke his leg last season because it makes it hard to tell where he really was in his value and development and whether it's reasonable to expect him to step up to the 1C role.
A second reason is his contract, and for a variety of reasons. While it's not a terrible contract it is large enough that if he trends downward at all during it then it starts really impacting a team that usually spends to the cap like the Rangers. They're probably looking down the road at players they need to sign and how to work out their cap space. Also, since his NTC would have kicked in, it was a valuable asset they had to move by a certain date in order to try to fill some other holes in their lineup.
Which leads into the third reason, overhauling their defense, prospect pool, and trying to acquire a power play quarterback. This was before Shattenkirk signed, obviously, but they still were obviously overhauling their defense on the right side with Girardi being bought out, Klein retiring (it was reported he was considering it before the draft and the Rangers had to have known as well), and it's been a constant refrain that they needed a PP QB. It's also known that they've been interested in DeAngelo since he was with Tampa, so they see the opportunity to grab a dynamic young offensive defenseman that they have liked for awhile, along with a top 10 draft pick, so that checks off a few boxes.
On top of that the Rangers have talked about shaking up their core a bit over the past few years, so while I don't think they necessarily wanted to do it just for the sake of a shakeup, I think they were more willing to make a move like this once they've decided they need to make more than minor tweaks to the team.
And finally...more speculation than anything, but they could be worried about Stepan's game declining. His numbers last year were on par with his usual but he had a poor playoff performance and is not a fast skater to begin with so they could be concerned that as he approaches 30 his effectiveness might decrease. Again this is more speculation than anything though. Also possible that they kept hoping he'd take the next step to be a 60-70 point guy instead of 50-60 and have waited long enough.
That said, yeah it leaves them with a hole down the middle. Their defense is a whole lot better and they have some promising pieces at center for the future now (their recent draft picks including Andersson they drafted with the 7th overall) but it's perhaps a role of the dice as to whether Zibanejad and Hayes can step up into the 1-2 roles and they can fill the bottom 2 center spots effectively.
I hope DeAngelo can continue to improve and be a good player for the Rangers...he's not going to be thrown into the fire now that they have Shattenkirk and Smith on the right but he'll have some competition with some other players in the system so he'll have to keep on his toes. Developing into a good PP QB and offensive defenseman down the road while Shattenkirk's contract expires is probably the hope.