It is pretty messy, yup. But there's a second half to the "Spellcasting" of 5e. Which is -how- they cast spells. Druids and Clerics cast from different lists which have different spells from Wizards. Wizards also have limited spells known while Druids and Clerics "Know" every spell but have to prepare them at specific times. Sorcerers know a limited number of spells, like Warlocks, and can't snag more from scrolls or prayer to change out on a daily basis, but Warlocks use their magic in a wholly different way, with access to fewer spells in a given period but potentially more over the course of the adventuring 'day'.
Spellcasting becomes a class-defining feature for each of these classes because the approach to spellcasting and the selection of spells create granularity between them. Create distinctions that your system lacks. A Cleric gets no inherent AoE damaging spells at level 1, while a Wizard gets a few to choose from of different damage types. And while a Cleric can Bane a group of enemies, he certainly can't grease up the floor under their feet, put them to sleep, or blind them with a dazzling array of lights.
I get the urge to create balance, but baby has gone with the bathwater, at this point. I'm suggesting you pull back a bit on the changes because it goes too far. Honestly, a Mage in your current system with the Life Theme makes a better cleric/priest/healer/acolyte/whatevertermyouwannause than your Acolyte does. Because when someone dies, the Mage can take a short rest and cast resurrection to get the person back into the fight without even the inconvenience of having the spell prepared or running back to town for a night's rest and a morning's prayer.
Just give them Spellbook at level 2. Have it be "Something they were working on" and poof it appears in their inventory at that point. Or have it given to them as a reward for doing something or whatever. A level 1 spellbook that does nothing is just a 50gp paperweight for the level 1 player who will probably have the lowest strength.
There are some words which are inherently insulting. Other words are descriptors which can be insulting but are often just descriptors. When I say "Bland" I'm not trying to insult your design, Mark. I'm trying to express a concept that's closest possible descriptor would be "Flavor" or "Texture". Right now, all the spellcasters "Taste" the same. Like American Cheese Slices. Perfectly cut and packaged slices of orange product that all have minimal flavor and are largely the same, even if one of them is "White Cheese" and another is more standard yellow. You can get the one in the blue package or the red package with the flames on the sides, but in the end the product inside is gonna be the same square in the same individual plastic wrapper.
It's not meant to be an indictment or an insult. Just a woeful lack of cromulent words.
The "Slow Ramp Up" isn't the issue. Having level 1, 2, and 3 each grant the same quantity of power is fine. The issue isn't that it's the same -amount- of power. It's that it's the same power.
Because it's not a CLASS defining feature. It's a SUBCLASS defining feature.
A Class defining feature is something all members of the same class get that differentiates them from other classes. Subclass defining features differentiate a given type of Mage from other types of Mages.
Barbarian Rage defines Barbarians as compared to Fighters. Fighters, as a class, don't go into a Barbaric Rage and attack their enemies with the fury of their boiling blood (Though you could create a Fighter subclass that does so). Ancestral Protectors define the Ancestral Guardian from the Berserker. Both Rage, and both use Reckless Attack, but they are distinct from each other in how they do so.
You misunderstand my apprehension, here. It's not "They're worried about a major feature" it's "They're looking at a series of options that don't appear to be at all distinct from each other". There's nothing grounded in the rules at level 1 to give a player an understanding of "OH! That's what Psionicists are and how they're distinct from Mages!" I could write you 3 pages of purple prose about how Barbarians are wild and raging foes whose raw emotions give them the strength to battle on. But if the only difference between Fighters and Barbarians is whether they're wearing heavy armor or not and a couple Hit Points the description ultimately means very little.
Class defining features (Like Warlocks using short-rest casting, specific spell lists that limit choices, preparation versus spontaneous casting) help a new player ground themself in what makes a Mage or an Occultist or a Psion into what they -are-.
I mean, take a look at the first line of your Naturalist class.
"Holding high a gnarled staff wreathed with holly, an elf summons the fury of the storm and calls down explosive bolls of lightning to smite the torch-carrying orcs who threaten her forest."
Is that a Naturalist or is that just an Elf with spellcasting ability who protects a forest? Couldn't a Mage or Occultist elf do the exact same thing by taking the same spellcasting themes? In fact of the four characters you describe as Naturalists, the only one that even hints at class-defining identity is the Half-Orc, but a Half-Orc mage with the Beast theme can do the same thing... so even that doesn't -really- make them distinct.
It smells like Gruyere, but it tastes like the previously mentioned American cheese slices. It's not crumbly or hard, it's not melty or damp, it's not tangy or spicy, it's just like the others.
Oh, no complaints. Multiclassing is mostly a tool for people to create particularly powerful characters by mixing class features together. I was just using it as a point of comparative power. If you did allow it, a Mage would get a whole lot more benefit multiclassing into a Fighter or Barbarian than an Occultist, while a Fighter multiclassing into Barbarian would get that same level of benefit. It's not a demand for multiclassing to be available, but to highlight the disparity of spellcasting as the "Class Defining" feature when it's completely interchangeable between all caster classes.
PROPOSED SOLUTION
With the system you have designed up to this point, the only suggestion I could make to add back that granularity would be Theme-Limiting or Theme Locking. Make it so that certain classes can't access certain themes, or that certain classes just -get- certain themes.
Giving players something "Free" at level 1, instead of limiting their options, is generally viewed more favorably, so I suggest having each spellcasting class have a specific theme, and then an archetype specific theme. So a Naturalist might get Beasts as a specific theme and then Storm as a theme for Druids (And reduce their magical insights appropriately). While all Ranger archetype Naturalists now only have Beast as their option for their 1 theme. Or give 'em a freebie.
For Psionicists you could make them all Telepaths and then give Psions Mind and Soul Knives Telekinesis in addition to any theme they might choose for themselves. You have to admit, it would make them into Psychics as a class definition and allow their archetype to define -how- psychic they are.