I am on board with "part casters" getting the same slot levels at the same class levels that full casters do. If a full caster can cast Wall of Force at level 9, then a part caster should be able to do so too, or at least have the option to do so.
Personally, I never play part casters because their lack of the high slot spells always disappoints me at the higher levels. Anything that is easy, at-will and always-on at low levels, is never powerful enough at the game-changing highest level. I look forward to the highest tiers. For example, I was enthusiastic about the character concept of the Artificer, but once the designers made it a part caster my interest in the class ceased immediately because I assume it will suck at the highest tiers.
If classes like Artificer, Eldritch Knight, even Ranger and Trickster, were getting full caster slot levels, like slot 3 spells at level 5, and so on up to slot 9 at level 17, I would play these classes − and probably enjoy them. It would be cool to do martial stuff, like sword and board, if there is sufficient high level magic along with it. For example, Arcane Archer could easily be a full caster Wizard subclass. But when 5e made it a part caster it became an instant no-go for me.
At least there is Bladesinger and Bard, who I enjoy as melee full casters.
(Ok, I really like the 5e Paladin. Via smites, it does so much magical damage that it FEELS like a full caster to me. Its auras are impressive magic too. The Paladin holds it own during the game-changing highest tiers. But now that 2024 seems set to "fix" the Paladin damage dealing, it might return to the "meh" of a part-caster feel.)
There is an important advantage when all caster classes gain the same slot levels at the same class levels.
Slots are pretty much the only game mechanic that defines other game mechanics for the highest tiers, from levels 9 to 20.
The low tier mechanics − like hit points, sword swings, cantrips, feats, ability checks, etcetera − are well understood, dealt with during almost every campaign, with exacting precision to measure how much each mechanic is worth.
But high tier mechanics − like distant teleporting, regenerating, attacking remotely, force-walling, at-will shapechanging, wishing, etcetera − are all kinda arbitrary guesswork. D&D historical mechanics collapse at the highest tiers. Even 5e spell lists for each slot are wildly uneven, with some spells in the same slot being either a waste of ink or so else much better that even spells that are in the higher slots. High levels are a mess. Even today. Think of how many times high level monster math gets tweaked. A mess.
When designing high level features for D&D classes and monsters, a designer often feels like climbing upward higher and higher on a rickety scaffolding. But the SPELL SLOTS are exactly this scaffolding. Designers compare every high level feature to the high level spells to guess how powerful a feature should be.
There is a benefit when part casters access the same slot levels as the full casters. The gaming engine necessarily becomes clearer and more robust at the highest tiers. Because now, there is a clear idea about the kinds of things every character SHOULD be doing at highest levels. If a level 9 full caster can cast slot 5 Wall of Force, then the part caster can too. And, importantly, the noncasters at level 9 should be doing features that are equivalent to Wall of Force in effectiveness, power and usefulness.
Moreover the part-caster classes will be choosing between powerful spell effects versus powerful martial effects. For a part caster class to balance alongside full casters and non casters, the designers need to understand exactly how much a spell effect is worth compared to a martial effect. This clarity of measuring all features at the highest tiers benefits, helps full casters and non caster balance alongside each other as well.
