I think it is a glaring omission because: a) The witch is important in Golarion (the most common non-divine caster) and b) the witch is an obvious primary occult caster, by not having it the bard was square pegged into the tradition and as a primary caster at the expense of other stuff. (IMO primal or arcane fitted better for the bard)
I get that you have a zealous appreciation of the Witch class, but I don't think you can make a strong argument that the Alchemist doesn't have a more compelling case for most deserving of the coveted 12th class spot.
This survey data from d20PFSRD, for example, has the Alchemist ranked 11th as the most played class, with the Druid coming in at 14th and the Witch coming in at 15th, with a whopping 1.2% difference between the Alchemist and Witch. (And yes, that is fairly large difference when you consider the sheer number of classes.) Plus, both the Oracle and the Magus outperform the Witch on this list too.
Also, I'm skeptical the changes made to the Bard that you mention are in anyway remotely connected to the absence of the Witch. The Bard (and other 6th level casters) was notoriously underpowered in 3e and almost a joke class. There was also a lot of positive feedback about the Mesmer, which was almost like an occult Bard, in their Occult Adventures lineup. And as it turns out, according to Paizo, their decision to switch the Bard to Occult magic was met with HUGE praise by playtesters. If people had been upset about this, then the Bard likely would have switched to Arcane.* So did it happen? Nope. And when I look through the Occult spell list, then it seems to fit well with the Bard. Will it fit well with the Witch too? Of course.
This is exactly what I least like about PF2. By making archetypes, multi-classing, and prestige classing all a single universal silo, there is a great homogenized feeling of the game. The worst part is making all three custom options compete for the same resource (class feats). The designer's have created a customization bottle neck and even admitted so during the playtest process.
I like what I have seen, though I understand that opinions will vary. I was a bit taken aback by this myself, but when I thought more deeply about it, I don't think it's that big of a deal.
Do these things compete with class feats? Of course, but how is this necessarily all that different from the prior system apart from how it is structured? If you were multiclassing or going into a prestige class, for example, then you would be relinquishing a level from your primary class where you likely would have gained a class feature or more spells so that you could get another (PrC) class feature instead. (And you likely would have screwed up the progression of your saves, BAB, or spells too.) Here you are continuing with your class but opting to choose essentially alternate class features from another class or an archetype. It's basically a more streamlined, efficient way of doing the same thing but without costing as much of a huge dip or loss in your class efficiency.
You can even do some things better this way than you could with PF1. Let's say that you wanted to be a Rogue/Wizard hybrid. I don't know what's optimal, but let's say Rogue 10 / Wizard 10. You are looking at having
BAB, 10d8+10d6 HD, and 5th level spells. If you start as a Rogue in PF2 and go full monty with wizard multiclassing, then you will still have 20d8 HD, probably more competitive class combat proficiencies, and up to 8th level spells. Plus, there is a 4th level Rogue feat that lets you combine Sneak Attack with spells, which was one of the biggest draws to the Arcane Trickster for magically-inclined Rogues.
