The idea is that the players are given the ability to enchant some blocks. Here are some ideas!
Please note that it is very hard to make an idea seem minecrafty, and many of these are probably bad ideas and would seem strange when actually implemented. I'd love criticism on the ideas though: I'm a game designer working on my own game and would appreciate any method of learning.
Dispensers - Power, Punch, etc...
Chests, Ender Chests, Barrels - Size
Shulker boxes - Size, Inception
This would allow us to put another shulker box in the enchanted one.
Hoppers - Size, Sorting
This would allow us to sort non-stackable items: The hopper would only accept the kinds of items already in the hopper. The enchanted hopper does not directly take the items: instead the accepted items would go directly to the block the hopper leads to. If the hopper leads nowhere, the item pops out.
Anvils - Unbreaking, Mending
The mending anvil would absorb XP orbs in a small radius.
The player could be given the ability to craft experience bottles, maybe in an enchanting table?
Pistons - Reach
Obviously this would allow the pistons to reach further. Has a few different stages.
Dispensers: I like the idea of adding bow enchantments to dispensers, but I'd rather see the enchantments come from using enchanted bows in the
recipe. And I think Infinity dispensers would cause a few issues, so I'd take that one out.
Ender Chests: That would definitely cause some problems since ender chest data is tied to the player and not the chest.
Chests. Barrels: Chests and barrels are already very efficient storage-wise. I don't think a size enchantment would be better than simply placing more.
Shulker Boxes: No. An ender chest full of shulker boxes already can carry up to 46,656 items. That's far more than enough for mobile storage. Especially for Inception. An ender chest full of shulkers that each is full of shulkers could carry 27x the number of items for a grand total of 1,259,712 items. That's not even mentioning how laggy storage that contains storage can be. Do it enough times and the game will lag out.
Hoppers: I already said Size wouldn't be better over simply adding more slots. I like the idea of Sorting hoppers denying all items that aren't already inside, but I can't really picture how it would function from OP's description alone.
Anvils: I like the idea of adding Unbreaking to anvils, but I think Mending anvils could get out of hand. Especially with XP farms. Iron is plentiful enough that it shouldn't be a problem to obtain more.
Pistons: Not enough description.
Luminescence in general: No. Everything you suggested already has a light level of 15. Anything more will cause any undead mobs in a 1x1x1 cube around it to burst into flames.
Beacon: No to Lumination. The other three sound interesting enough, but they all seem to rely on the Reflection enchantment. Reflection itself seems useless since beacons can't function if there are any solid blocks in the way of the beacon. Downward always has the Void, and horizontally always has unexplored/unreachable chunks. You'd need to add an entirely new block that can "end" the beacon beam while still allowing it to function.
Scaffolding: Honestly, I've never used scaffolding before. I can't talk about it, as such.
Bed: Safety sounds rather pointless. If you're far enough into the game to be enchanting beds, you should be strong enough to clear the area before trying to sleep.
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If you'd like to talk with me about other games, here are a few I play.
Team Fortress 2
Borderlands series (Borderlands 2 is my favorite game, ever. TPS combat is a lot of fun and makes up for the lower-quality story, in my opinion)
Elder Scrolls series
Warframe (IGN is something like That_One_Flesh_Atronach)
Pokémon series (HGSS forever)
Left 4 Dead 2 (Boomer files always corrupt though)
SUPERHOT (SUPERHOT is the most innovative shooter I've played in years!)
Dead Rising series (Dead Rising 2 is one of my favorite games, and the 3rd was a lot of fun. 1st has poor survivor AI and the 4th is bad)
Just Cause series
Come to think of it, I mainly play fighting-based games.