It was stated in a early chapter that one MS Obito cannot use both form of Kamui at once solely due to the fact that it is the same technique applied differently.
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This means the with one eye, Obito wasn't able to warp while intangible because it the same Kamui used on his body in a different way. An analogy: deva path can't use Shinra Tensei and Basho Tenin at the same time. Why? because it's the same technique.
Since that is the only reason, then with double MS, Kakashi can use intangibily and Kamui snipe at the same time. This works because of double MS.
One eye can use intangibility and the other eye can use Kamui snipe. They don't logically interfere with each other
It's a perfect system. He can make his whole body intangible except for the eye performing Kamui snipe.
Yes he can use them both as you said but there is no sniping, Kakashi already stated that he had to be very close to use Kamui snipe since that eye was going blind
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. So regardless Kakashi would have to wait until he's right up in a person's face to use it as he had to be right there by Madara to use Kamui. Also if Kakashi is intangie and Say Sasuke used Amateraus as Kakashi tries to Kamui snipe, Kakashi would warp the Amaterasu to the other dimension which would hit his body. If Kakashi throws Kamui shuriken via PS then some one like Naruto, Minato, Tobirama, Madara, or Hashirama who uses shadow clones can have their clone take the Kamui shuriken and when a Kakashi tries to go intangible they deliver a killing blow. Of course only Naruto actually knows to do that since he actually did it to Obito with his Rasengan but you get what I mean. Point is Kakashi can't snipe anyone long range, he needs to get up close and be able to track his opponents movements which he can't do for speedster A's speed level+. Also should point out that Kakashi doesn't know about the 5 mins limit on the intangible Kamui so for someone like Nagato, Konan, and Madara who knew about or someone who can come up with there having to be a limit, that lack of information can cost him. From what we see DMS Kakashi can't last long, he closed his eyes before Naruto and Sasuke actually beat Kaguya and he fell over after Obito left him. Obito can't stay there long so if a Kakashi can't take out his opponent in that short few minutes then he will be left defenseless plus it was Naruto who brought Obito back in the first place as a Kakashi said here
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.So I see no reason to argue what he can or can't do when we know there's certain things he can't do, he has a limit for the temporary power, and in vs against Naruto since he brought Obito back he probably can sent him away.