Archetype cards you wish they would add to LoR.

Honestly I'm surprised they don't have any dredge like cards that use your graveyard as a resource. They have a ton of discard cards but nothing to bring back discarded cards outside of deep.

Cards like that would really help champs like Jinx be more viable. Also you could build decks that discard expensive heavy hitters early on only to bring them back later during the mid game like turn 5 or 6 for cheap.

You could also take that as a way to add mill cards and cards to discard cards your enemy has in their hand or deck and even use your dredge cards to take from their graveyard too.

We have a few cards that can use the Graveyard:
The Harrowing, Kalista, The Rekindler, Mist's Call

Allowing too much use of the Graveyard as resourse is a dangerous move.
Modern Yu-Gi-Oh! is the best example as it uses the Graveyard all the time for plays and look how bad their metagame became. 

Also keep in mind Runeterra has the spellmana system. That could allow some degenerate power plays. Example: not playing anything on T1/T2 to store 3 spell mana; then play Get Excited! to discard a big unit; ressurect it with an effect similar to Mist's Call and attack RIGHT AWAY as this game don't have summoning sickness. 

Quote From Hellcopter

We have a few cards that can use the Graveyard:
The Harrowing, Kalista, The Rekindler, Mist's Call

Allowing too much use of the Graveyard as resourse is a dangerous move.
Modern Yu-Gi-Oh! is the best example as it uses the Graveyard all the time for plays and look how bad their metagame became. 

Also keep in mind Runeterra has the spellmana system. That could allow some degenerate power plays. Example: not playing anything on T1/T2 to store 3 spell mana; then play Get Excited! to discard a big unit; ressurect it with an effect similar to Mist's Call and attack RIGHT AWAY as this game don't have summoning sickness. 

Do any of those cards work on discarded cards? Really do want to know. Because that would make them a ton better.

They don't, thats the point.
Unlike other card games, discarded cards don't go to the Graveyard to prevent ressurection abuse like the one i listed.

The game had a ton of keywords from the get go.  It's normal that they didn,t put everything. You must have something that will bring new stuff from expansions.

I would like to see something like MtG slivers, where cross-regions units synergize in interesting ways.

More specifically: I would like to see them take the Elite tag, dilute some of the population out of Demacia and add it to a few of the ubiquitous / underutilized cards in other regions, and then add new cards into the rotation that do interesting things to allied elites, e.g.:

• Noxus: Elite Veteran; whenever an allied elite survives damage give it +1/+1
• Demacia: Elite Armorsmith; give all allied elite Tough
• Ionia: Elite Priest; whenever an allied elite is summoned give it Barrier
• Frejlord: Elite Warchief; give all elite overwhelm 
• SI: Elite Horror; when an all allied elite dies, obliterate the top 3 cards of your opponent's deck
• P&Z: Elite Scientist; when played summon a copy of target elite
• Bilgewater: Elite Mercenary, whenever an allied elite is summoned, give the strongest enemy vulnerable

Don't get caught in the specifics or balance, that's just a rough sketch.  The idea would be that it would actually be interesting to homebrew / tinker with unusual region combinations because you'd be inventing new synergies.  And unlike the original slivers in MtG, you're hard-limited to just 2 regions so you can't just splash everything to build an invincible army.

I'd like to see some kind of healer ally, that regenerates the most damaged ally at the end of each turn.

Or a wall unit that can't attack but is a really good blocker. 

Also more cards with effects that occur when you have no cards in hand. Or 10 cards in hand.