The problem with adding new classes is that, really, WoTC seems determined to focus on subclasses first and foremost.
That’s not really a problem so much as wizards just being obstinate. Nothing within the game framework is actually prohibitive of new classes.
Gunslinger? Take an Archery focused Fighter, Ranger or Rogue, give them a gun, let them make ammunition with an Int check and access to the raw materials, and you're done. At best, we could get some gunslinging-archetypes for more guns & sorcery campaigns. Heck, I'd actually be kind of interested in a Hexslinger warlock or a Holy Gun paladin.
Could work, but you’re also going to either need homebrew stats for the weapon or use the examples in the DMG. Then you’re going to need to clarify which feats/class abilities apply to it. Whether or not this is too much work is a case-by-case basis, but I think it’s part of the underlying desire for new classes; the idea that all that stuff has been checked and evaluated.
Summoner? The Conjurer already exists and is focused around being excellent at commanding summoned minions; how would this honestly be any different?
If the conjurer had anything to do with the fantasy of controlling minions (especially long term) I might, agree, but it doesn’t. Minor Conjuration and Benign Transportation are mundane utility and mobility perks respectively, and Focused Conjuration doesn’t deal with minions specifically. Only the 14th level feature directly contributes to the fantasy of summoning creatures to fight for you.
Oracle? This'd be very hard to make different from a "Cleric-dabbling" Sorcerer subclass, ala the mk2 Favored Soul.
Agreed, especially with the new favored soul, diviner, and your preferred blend of cleric, this one is pretty much covered.
Shaman? A Sorcerer that "dabbles" in Druid magic.
Not going to cut it, doubly so if you preferred the 4e shaman as opposed to the general theme of shamanism. Aside from cantrip scaling you’re going to fall on either side of being either mostly a sorcerer or mostly a druid.
The Gish archetype? It's not quite as satisfactory as 4e's Swordmage, personally, but between the Eldritch Knight Fighter, the Bladesinging Wizard and the Stone Sorcerer, it's covered.
Stone sorcerer is garbage, but the other two work well enough, letting you pick between a magey fighter or a fighter-y mage. They really could recreate the swordmage pretty easily with eldritch-knight specific spells or abilities.
Warden? Without 4e's mechanics to really help make it feel unique, ultimately, this is a Druidic version of the Eldritch Knight Fighter.
We already basically got warden though, between either a nature themed paladin or the new guardian from the ranger UA. This one I agree is pretty unnecessary at present time.
Investigator? We have this already - it's a Rogue archetype.
I…have actually never seen this one called for personally.
Bloodrager? It's a Sorcerer/Barbarian fusion subclass.
And would be terrible. It’s incredibly MAD, needing STR, DEX, CON, and CHA. Oh yeah, bonus points, right under the rage feature it qualifies that you can’t cast spells or even concentrate on them while raging. This multiclass doesn’t function towards the desired archetype in any way. I don’t know if this is full class worthy (I don’t think so), but it’s certainly not doable at present with the current class rules.
I literally can't think of anything that WoTC couldn't jam into the subclass mechanic and make it work, except maybe psionic classes - and odds are likely those'll all end up as subclasses of Mystic.
I think there have been multiple examples given, the most popular and recurring of which of course is the warlord.
Don't forget, WoTC took a poll on Prestige Classes and, from what I was told, the response to their return was overwhelmingly negative. It's not hard to imagine that, from that, WoTC may also have concluded that people would rather see ideas fit into the subclass framework first before trying to make them into full-fledged classes.
Which is unfortunate, since themes like the Bloodrager are really only going to be effectively done through something akin to a prestige class. It also means Wizards will waste time with things like the artificer subclass, which did not live up to expectations at all, and was much better when it had the framework of a full class to expand upon.