I like to say kamui isn't a dimension, but rather a doujutsu to cross them. Its descended from sharinnegan anyway so its not at all strange it can go places, that dark one just is what it has a particular affinity with for whatever reason. Nevermind the silliness of the idea that an entire dimension came into being each time a kamui mangekyo was formed, I do have a few reasons I think there's only one of them.
Kamui can teleport you around, meaning the dimension you go to clearly overlaps enough with the main one for you to be able to move around. If it was limited to your eye only, you'd be able to swoop in and out just on the spot, since after all, your eyes can't exist everywhere in the world at once >_>;
Another bit is the intangibility. The overlapping part is phased to the other dimension, yet not entirely, since if it was you'd have just ripped a gaping hole into yourself and most likely committed suicide. Sketchy as hell, but about only way at least I can see it working again is that its its own full dimension that overlaps with this one, allowing you to phase out a part just enough to turn intangible, yet not completely so you don't get rekt by your own jutsu. If you were sending stuff inside your eye instead, I can't really imagine another outcome than just a bloody mess.
Lastly the fact you can go elsewhere with it, especially with both eyes. Being eye specific would mean you can only get in and out of there, but nope, if you synchro with somebody you can follow them even from afar, appear in there about where you wish instead of with the person. Top it off you can even go to 'kamui' dimension and come back there too, proving you can basically go anywhere as long as you know the location and have the chakra. Hell, with both eyes you can even literally rip a hole open to physically see into the other dimension. If it was eye specific in turn, most you could really do in another dimension is just hide in your eyes, basically get in your own pocket in someone elses pocket, pocketception.
Summarized, I believe every kamui type mangekyo by default goes to the same dimension, which quite closely overlaps the main one. And due to this overlapping is why I believe its so easy for them too, as opposed to going into other ones. Obito did mention himself of Kaguya's places being 'incredibly far', so he'd need significantly more chakra than he had to get to it.
So to close on my view of the kamui thing, if a kamui user takes another user into the dimension, it wouldn't really be any more difficult to get out than to just wormhole yourself out.
To briefly address hiraishin, I believe it only really briefly pops you out of this dimension, to a kind of border realm like rinnegan's limbo, then back out again, not into a whole other dimension. Since that'd mean you kinda still are here even as you poof, you'd only really be able to do it inside that dimension, so if you got taken to 'kamui dimension' you'd be stuck teleporting around inside there only. You'd have to get help or make some non-canon jutsu of your own with it, and that's a whole new can of worms.
Summoning I can't say much about, since while known info suggests its basically the same as hiraishin, moving stuff around only inside the same dimension, Hagoromo and kages did summon the bijuu and team 7 out of Kaguya's dimension. However, Hagoromo did mention he was going to do some specific special jutsu for massive chakra amounts, not just a typical summoning, so its highly likely this was either some special rinnegan-only thing if not even Hagoromo's own unique techniques.
Edit: reread the few panels, looks like the special technique was bringing kages back without edo tensei. The fact both Hagoromo and Sasuke were able to pierce into other dimensions though, and not really anyone else, implies its a rinnegan/sharinnegan talent. I imagine Hagoromo made the connection while the kages supplied the power, whereas Sasuke used his own power which led to his eye power weakening temporarily due to how draining it was.