Before we get into the neutral legendaries, I want to make a quick note about Genn and Baku. These cards both generate their hero power-altering effect at the start of the game, but ask you to build your deck using exclusively even or odd cards respectively.
It’s easy to make a case why these decks will be weak. All you have to do is look at a class, pick an odd/even cost card that’s good, and say, “If I don’t put this in my deck, it'll be terrible”. But that's the same sort of thinking that saw people sleep on cards like Reno Jackson and Prince Keleseth.
To understand the value of this kind of effect, you need to figure out what kind of deck would most benefit from the improved hero power, then work out which correctly-costed cards support that archetype. Yes, the downside of these cards is real, but the upside is substantial.
Baku the Mooneater: Upgraded hero powers are not equal across all classes. There are two that stand out as being premium: Hunter and Warrior. The former is the most proactive hero power in the game, allowing you to close games out, while the latter is the most defensive in the game, capable of being useful even when your hero is at full health. I could easily see Baku helping to define an aggressive hunter or quest warrior list. Warrior specifically might like it more because Tank Up has already proven its potency, and has positive side effect in making Reckless Flurry into a much better card.
Rating: 8/10 (High potential)
Genn Greymane: When playing Greymane, you will be using your hero power on turn one. In terms of classes that can benefit the most from that, Shaman and Paladin spring to mind. Being able to always have a body on board on turn one is quite appealing, as is being able to weave in more small bodies throughout the game. Constant board presence means cards like Defender of Argus, Sea Giant, Flametongue Totem, and other conditional buff effects start to look especially attractive. Whether these will be the best decks in Paladin and Shaman is another question.
Rating: 7/10 (Has potential)
Azalina Soulthief: Beyond the inherent fun of stealing stuff (hello, Priest mains) the best way to think of Azalina is like Divine Favor on a small body. The goal is to just empty your hand by around turn seven and then, just as you’re running out of gas, drop Azalina to snag a few cards from your opponent to keep going. This might even work, given that the cards you pick up are likely to be the more expensive threats your opponent hasn’t been able to play since they’ve been answering you. The obvious is problem is that it won't be good against aggressive decks, which are usually looking to have closed the game out by that point. Azalina is worth keeping an eye on, but doesn’t seem meta breaking.
Rating: 5/10 (Too average)
Dollmaster Dorian: When looking at Dorian, the obvious question is whether you can abuse his ability. Given Dorian's effect and statline, he doesn’t seem like the kind of card you can drop on the board and hope it will stick as part of a game plan. That means you need to be ready to draw more cards as soon as you play. Tutor cards—think Elven Minstrel and Sense Demons—seems appealing for finding the right targets (if you haven’t already drawn them), but that also costs an extra chunk of Mana, making for a tricky combo. You can also think about board-based draw (like having a Loot Hoarder in play), but there's no guarantee of finding the right targets reliably unless your deck is full of them. Dorian might also work in a Deathrattle shell, as the copies will be useful, but there's also a chance it just won't have enough synergy with any meta decks. Nonetheless, a very cool card, with lots of potential, but likely hard too hard to extract value from in practice.
Rating: 5/10 (Too average)
Countess Ashmore: This lady rocking the stylish millinery is the new Curator-style minion in the set, and she shows a great deal of promise. Countess Ashmore's main strength lies in the fact she is both neutral and, unlike The Curator, capable of cards other than minions. This is a big deal, as it allows Ashmore to tutor for spells and weapons in addition to whatever minions you may wish to search for. Her body is large enough that she can’t be ignored, and if you can draw even two cards with her she is easily in the range of playable. This is the type of card that only gets better over time, as the range of options in Standard increases. The question becomes what cards those might be, as many classes lack access to playable versions of all three card types she draws. My main picks are for Warrior—as she adds gas and board presence to the Tempo deck Blizzard seems to be pushing pretty hard—or Warlock, which can find cards like Spellstone or even Drain Soul, as well as Voidlords, Lackeys, or Plated Beatles. The larger question there is whether Warlock will have room for her.
Rating: 8/10 (High Potential)