Wow, where to begin? The amount of dead archetypes is enormous!
Frozen Giant mage MurLock Freeze Mage Deathrattle Zoo Huntertaker Miracle Rogue SR/FoN Combo Druid Mech mage Secret Paladin Flamewaker tempo mage Patron Warrior Anthonidas OTK mage All C'Thun decks Spell hunter Midrange Shaman Kingsbane Rogue Malygos rogue Shudderwock shaman etc. etc. etc. just from the top of my head.
BUT, there are also more new archeypes becoming viable and old ones returning with more support. Recruit Paladin lives on as Odd paladin in Wild, for example, with Quartermaster still being the most powerful play in the deck. Ramp druid is still alive, even though it has changed a lot during the years. Malygos decks are still returning regularly, and slow, defensive warrior decks and Zoo-ish decks are usually a thing.
Well thats because blizzard does 1 set arch types intentionally like Jade and are meant to get a set then never be heard from again not so much dead just as intended time removal
all though just in base set we have so many half*** types just in that like discard warlock
Looking at the above mentioned archetypes I think the reasons usually stem from either the interactivity of the archetype/style and how extra support would affect Wild Decks.
With Silver Hand Recruit (Odd Paladin) and Handbuff Mech Paladin they are currently Tier 2 I believe in Wild but any support that would make them relevant in Standard could potentially push their power level too far in wild. Murloc Paladin probably has more room to develop but still with access to all Murloc Cards even 1-2 strong support cards can greatly increase the power level in Wild.
I think HS Designers have previously mentioned the gameplay limitations with Freeze Mage (lack of interactivity and often unfun to play against). Any more board freeze cards would again make Freeze mage a nightmare for Wild, probably even worse than the potential Paladin decks.
Big Demonlock is one of my favourite decks, but the printing of Bloodreaver Guldan really limits the design space in Wild which again will effect support received in newer sets. Renolock/Demonlock variants have pretty much been tier 1-3 in Wild since Bloodreaver Guldan was released and I believe it's why we haven't seen another powerful big demon in a while like Malganis. They did add a new one in Scholomance so i think their is room for more but any demon support that would be relevant in Standard could again push Demon decks over the top in Wild.
OTK decks also slightly suffer from this as they revolve around clearing and collecting your combo pieces for OTK. I like OTK but I believe designers look to avoid these decks being too relevant/powerful as losing too many games from OTK's is also considered 'unfun' and 'un-interactive'. If you notice the current Malygos Druid has a lot of minion based interaction in the deck despite that and probably falls in the realm of what is okay for an OTK deck.
This is mostly my understanding from what I've heard from designers as well as some players, in reality it usually comes down to how 'interactive' and 'fun' is the archetype, and how will the Wild Format limit their design space.
I think the best that might come is support that does a similar thing to previous cards in that archetype more so replacing them rather than creating something really new, as in that sense Wild players will have to make a decision over whether new or old support cards are better rather than running all of them.
Just my 2 cents but I would say that Blizzard can be inconsistent in regards to what they consider 'problematic' or not.
Silver hand recruit Paladin (Why did they stop supporting silver hand recruits?)
Murloc (We did have murloc paladin on ladder last expansion but it wasn't very competitive) (oh and I miss Finja)
Mech (they were cancer)
Freeze mage (We don't have a classic style freeze mage but mage still runs a lot of freezes anyway)
Competitive otk decks. Malygos Druid being the exception.
Big demon warlock/ handlock
Mill rogue
Jades
Secret mage (not sure if its a thing )
Edit: Silence priest
We need a proper handlock for years now
Not the type to cheer for Blizzard, but they're actually doing good work when it comes to archetype rotation, and decks diversity...
This said, I'd like to see control paladin come back someday.
Aggro rogue, tempo demon hunter, bomb warrior, highlander mage, face hunter, zoo Warlock wow so much deck diversity
Keymaster Alabaster come faster
I miss the old dragon priest..
Play wild :)
Take a walk on the wild side...
Midrange Hunter, Aggro Mage, Control Paladin, Control Mage, Combo Priest, all came to mind.
Wow, where to begin? The amount of dead archetypes is enormous!
Frozen Giant mage
MurLock
Freeze Mage
Deathrattle Zoo
Huntertaker
Miracle Rogue
SR/FoN Combo Druid
Mech mage
Secret Paladin
Flamewaker tempo mage
Patron Warrior
Anthonidas OTK mage
All C'Thun decks
Spell hunter
Midrange Shaman
Kingsbane Rogue
Malygos rogue
Shudderwock shaman
etc. etc. etc. just from the top of my head.
BUT, there are also more new archeypes becoming viable and old ones returning with more support. Recruit Paladin lives on as Odd paladin in Wild, for example, with Quartermaster still being the most powerful play in the deck. Ramp druid is still alive, even though it has changed a lot during the years. Malygos decks are still returning regularly, and slow, defensive warrior decks and Zoo-ish decks are usually a thing.
Editor of the Heartpwn Legendary Crafting Guide:
https://www.hearthpwn.com/forums/hearthstone-general/card-discussion/205920-legendary-tier-list-crafting-guide
Well thats because blizzard does 1 set arch types intentionally like Jade and are meant to get a set then never be heard from again not so much dead just as intended time removal
all though just in base set we have so many half*** types just in that like discard warlock
I would say combo and control are pretty dead.
Galavant Animation
Not completely dead, more of a niche. I hit legend with a control highlander mage this season.
Looking at the above mentioned archetypes I think the reasons usually stem from either the interactivity of the archetype/style and how extra support would affect Wild Decks.
With Silver Hand Recruit (Odd Paladin) and Handbuff Mech Paladin they are currently Tier 2 I believe in Wild but any support that would make them relevant in Standard could potentially push their power level too far in wild. Murloc Paladin probably has more room to develop but still with access to all Murloc Cards even 1-2 strong support cards can greatly increase the power level in Wild.
I think HS Designers have previously mentioned the gameplay limitations with Freeze Mage (lack of interactivity and often unfun to play against). Any more board freeze cards would again make Freeze mage a nightmare for Wild, probably even worse than the potential Paladin decks.
Big Demonlock is one of my favourite decks, but the printing of Bloodreaver Guldan really limits the design space in Wild which again will effect support received in newer sets. Renolock/Demonlock variants have pretty much been tier 1-3 in Wild since Bloodreaver Guldan was released and I believe it's why we haven't seen another powerful big demon in a while like Malganis. They did add a new one in Scholomance so i think their is room for more but any demon support that would be relevant in Standard could again push Demon decks over the top in Wild.
OTK decks also slightly suffer from this as they revolve around clearing and collecting your combo pieces for OTK. I like OTK but I believe designers look to avoid these decks being too relevant/powerful as losing too many games from OTK's is also considered 'unfun' and 'un-interactive'. If you notice the current Malygos Druid has a lot of minion based interaction in the deck despite that and probably falls in the realm of what is okay for an OTK deck.
This is mostly my understanding from what I've heard from designers as well as some players, in reality it usually comes down to how 'interactive' and 'fun' is the archetype, and how will the Wild Format limit their design space.
I think the best that might come is support that does a similar thing to previous cards in that archetype more so replacing them rather than creating something really new, as in that sense Wild players will have to make a decision over whether new or old support cards are better rather than running all of them.
Just my 2 cents but I would say that Blizzard can be inconsistent in regards to what they consider 'problematic' or not.