My idea was you'd pass the coordinates of the right click action or something like that. (so it'd probably act weirdly if you used some form of "remote clicking" from another mod) Not that having a tile entity would be any problem that was more a descriptive thing.
My main worries are things like GUIs using the same global variable for things and conflicting, or the last one to open grabbing all input, or not being able to differentiate GUI-opening form other right click actions, etc. The only things making me suspect it's possible at all is the NEI and that one sorting mod seems to open their GUIs simultaneously as arbitrary others, and that you can set different GUI sizes that have different offsets already.
Also, obviously the more custom interfaces like Thaumcraft and MPS are going to be troublesome. (and thaumcraft would be one of the things it'd be especially useful for so it cant be just ignored) Also, because of the said rebuilding of it manually of the player inventory each time, not getting 8 badly synced duplicates of it taking up most of the screen might be impossible without custom code for each block or relying on some standardization I don't know about.
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Hmm, I had another mod idea today (that probably will never be made, since I have better ones from longer ago if I ever get around to modding myself). Basically, I were thinking about that once you've made one set of the best armor and weapon, you never really make any more unless you lose it, which leaves many mods unexplored. Similarly, you tend to make one tiny bedroom, and all the rest of your base is just big workshops and industries. Also, there is no use for things like buffing splash potions and the like currently.
So the mod idea, one block and one entity. Several various ideas for the block, called a "barracks" but basically it either is a kind of door and detects nearby doors. Then it searches for a room that fulfills the requirement of 1) only exit is that door, 2) has a bed, 3) has a chest with food. It will then spawn the entity after a while randomly, consuming the food, equip any armor or weapon in the chest, and stay in the room seeing to sleep in the bed during nights. Then, it'll start to follow you if you rightclick the barracks and fight for you. So basically like many of the clone and recruiting mods out there, but focused on logistics (housing, food equipment) of mass armies rather than leveling individuals, and balanced for automation.
(obviously afterwards you could trow in extra stuff like item usage on any level higher than zombies have, or different versions of the mob depending on the type of food)