I broke down the different investigators into different stat line categories for discussion:

12 stats/14 HH
Skids, Agnes, Daisy, Mateo, Finn, Leo, Marie, Minh, Norman, Roland, Sefina, Silas, Ursula, Wendy, Yorrick

12 stats/15 HH
Jenny, Rex, Zoey, Jim

13 stats/14 HH
Akachi, Mark

11 stats/15 HH
Carolyn

Special Cases:
Calvin, Lola and Ashcan

I really want to talk about why these small variations exist.

First off, Carolyn, this isn't to weird for me, -1 stats for +1 health/sanity seems like a decent tradeoff.

I am still perplexed as to why the Dunwich line gets +1 to their health/sanity. Sure they don't have a secondary class, but I don't understand why that is much of an disadvantage. All the roles have good cards. Plus the 5 card splash makes up a lot of ground. Their signature cards are good and their sig weaknesses are not out of line with the core investigators. Even their abilities and elder sign abilities are good/synergistic. Okay Jenny's Elder Sign ability isn't good, but her ability is out of the park.

Onto Mark and Akachi. I sort of get Mark as Sophie can give him a -1 to all stats and/or it allows Sophie to boost his 3s to a 5. Akachi though I am not getting at all. Again, her sig cards are not weaker than others and her ability and elder sign is good as well. Plus she has decent deck building options (not a secondary class but still).

I get most of the one offs. Lola is weird. Having a large card pool is one thing. But having only 12 in health/sanity is rough and her special ability is basically a weakness/way to mitigate a weakness. Don't get me wrong, I like the one class at a time situation, I just don't get why she couldn't be 7/7 instead of 6/6.

Maybe its just my take that more options in deck construction do not necessarily mean a more powerful investigator.

Thoughts?

I think that you're pretty spot on with your assessments, but I believe in the case of Akachi and Mark, since their other primary pool is dictated by trait, this severely limits their deck options. Generally, these characters are so themed at their core around their faction, that the traits that they have access to almost always have a large number of them that are already in their primary faction pool. For example, most tactics are guardian cards already and most 'charges' and occult cards are going to be in the mystic pool. This means they are even more limited than you would first think. This may change as more cards enter the game.... but they could stay proportionally limited. I expect this to be true of Rita (I favor the idea that she will be a survivor with 'tricks' which have a large portion that already fall within the survivor faction).

Splash cards of any type are also limiting when you can only take 5 in the case of the Dunwich friends, especially if you like to optimize your decks with 2 of each unique card of your standard 30 cards. And if double faction cards like the Grisly Totem DO count as 2 of your splash slots per 1 card if it is out of faction (soooo Zoey/Jim/Jenny for grisly totem), that puts them at another disadvantage, only allowing them TWO dual-class cards if it is outside of their other restrictions, and 1 other out of class card.

I think part of Lola's balancing also includes the fact that her deck can include 5 more cards than a standard deck, which is extra strong when you consider that her requirements are a lot less limited as well, but I'm not sure she needs to be 6/6 either. And notedly, Sefina has stats in-line wih other investigators and does not suffer for her extra 3 cards she receives.

I personally think Carolyn is a bust as far as design goes (but this is based on the replacement cards). Foolishness is a rubbish signature asset since it takes an ally spot and requires you to spend actions and/or resources to make it useful. I don't feel like the stat hit was necessary. That being said, I also refuse to play her again until she has an option other than To Fight the Black Wind.... so I don't know what they're going to do with her non-promo signatures in order to make her statline not horrible because the justification in it really seems to come down to having Foolishness. I suppose that assessment could be wrong though and we may see that 'healing' investigators use this template because FFG thinks they will provide a stronger role as more coming cards are introduced. I expect one day we'll get a Vincent Lee investigator who can take cards "that heal damage" and we'll find out if he has similar statline hits.

In the end, it seems like the more restricted your pool, the better your stats in most cases. I don't know that more severe restrictions makes your character innately less powerful, but it might make them less likely to be top-choice if they have stats akin to everyone else in their primary faction. It gives the player another element to consider when deciding whether to go full guardian Zooey or full guardian Mark, for instance. If you want to slot more out-of-class cards to round out or make your deck more flavorful, it comes at the cost of the extra stat point that Mark has (granted Zooey has more 'sanity/health' points). I like it in some ways, because it gives each investigator even more identity without feeling entirely out of balance.