I will preface this by saying, Inferno and Stunt Double could be higher (Inferno has a good base toolset and Stunt Double isn't complete trash possibly) I'll go character by character for ya.
Lackey
So what can I say about Lackey. He's got meh armor. He has no great plus frames. Sure he has good buttons and good damage but he has so many anti-synergistic things in his toolset it's baffling. He is clearly supposed to be up close and personal, yet his command grab throws the opponent full screen. Basically what this comes down to is that, Lackey doesn't have the correct tools to be playing this game. He has a great basic toolset that has potential to be a real formidable force in this game but his dirt just isn't strong enough to compete which causes him to suffer in a good amount of matchups.
Warrior
See my explanation earlier in this thread. Also, just because you have a safe wakeup doesn't mean you aren't trash. That notion is not logical.
Marksman/Outlaw
Outlaw is a garbage fire. Marksman is a slightly less hot garbage fire. They have gaps everywhere. One of them is unsafe as hell, the other one relies too much upon stamina to make himself safe which in turn makes him unsafe for a large amount of the match. Marksman's "zoning" is trash, Outlaw gets zoned out absurdly easily. The character has one okay mid and okay damage. His mixups are laughable (granted, i guarantee you everyone on of you has been hit by the new slow overhead at least 10 times if you've played against the character enough) They just don't have any good or even decent tools to be competing in the game.
Heavy Weapons
Oh boy. The odd one out of the Jax variations. He got hit, absurdly hard by the stamina changes. He lost his easy midscreen hitconfirms and is now having to be reliant on either not run canceling for his hitconfirms or having to link into S3 which is a link that is so tight it makes coals into diamonds. And his "pressure" is the worst of the three variations. Granted he can mix you and cancel pokes into specials and make you respect his stuff with staggers but like...he has terrible armor, he doesn't have the purple wave to help with his mind games. He gets zoned out. Any bad matchup that the other two have is increased by a ton on Heavy Weapons. The character is just bad.
Pretty Lady
The character that I am definitely most qualified to talk about in Tier 4. Pretty Lady is a zoner with some pretty bad projectiles. Every saw has terrible recovery frames on whiff so you jump one saw and you get in almost for free. His up close game is pretty bad considering his lack of mids and his lack of good follow up to his frame trap with EX Up saw. He has terrible whiffing issues on almost half the cast. So basically what you have is a zoner who can't zone as well as the other zoners in the game and doesnt have an up close game to compensate for it. It's just a mess.
Venomous
Venomous is weird. This is a chip/tick damage character...who's chip damage is unsafe. Venomous has some good armor and some good damage sure, however, the issues that plague d'vorah are all there and Venomous has little to nothing to make up for that. It's basically variationless d'vorah with a little more damage and a decent armored move. Very lack luster.
Tarkatan
This character got gutted. When patch day came, I figured he might be like mid tier afterwards but nope, this character is just a flaming pile now. He is completely unsafe on everything he does (EVERYTHING) He just has way too much risk with very little reward. He's just a bad design with TERRIBLE frame data now. Poor Baraka.
Kenjutsu
This one won't take much to explain. His push is bad. His armor is bad. He's got 50/50's but one half is non-hitconfirmable and unsafe and the other one is harder to hit confirm and is unsafe if not hitconfirmed. He's got the same whiff recovery problems the other two have but not the same things to make up for it *shrug*
I agree that having a safe wakeup doesn't preclude a character from being bad, especially when they're completely and easily counterable.
Now, after reading your new ordered tier list, I'm about to do something I've literally never done. I'm going to up play my main, Venomous, because I'm not sure she's actually bottom 5. Venomous is definitely down there, but despite all her design flaws and your accurate assessment of her playing like a higher damaging variationless D'vorah with ok (if counter intuitive) armor, she's too functional and her normals are too strong for her to be quite that bad.
I think one of your misconceptions is that she is a chip/tick damage character. Before it was nerfed, I'd have agreed with you, but the spray has been nerfed far too many times at this point. At this point, a block string into spray does maybe 2.5% more damage than most other block strings into specials. It's not really anything special, and since you'll pretty much never land enough pokes in the neutral in a short enough time frame to get a meaningful stack bonus, her poison is really more flavor than anything else. The supposedly central tenets of this variation are just minor features outside of combos, which is just sad honestly.
In my opinion, she's more of a grappler that doesn't have a command grab. Her grabs also add a single stack of venom, leading to a minimum of 13.5% damage per throw. They certainly add up, but more importantly, allow for strike/throw mixups. As you've stated Venomous has good damage, though it's mostly off her high strings and f44. In the corner, any of those can lead to 46-49% meterless damage or 30% restands, and this is on top of the standard overhead/low corner set play.
Is it just me, or did I try and highlight the strengths of Venomous and still make her sound bad? Feels like my whole defense is that even though she's poorly designed, she has a good mid, no serious whiffing issues, and is pretty good in the corner. Bottom 5 it is then :/