The problem, as I see it, is that while the bard might be balanced against the wizard at levels x, y, and z (assuming they get balanced features to make up for the gap in spell level progression), as soon as they get to level (z+1) and gain a new level of spells they're arguably imbalanced, because they have spells just as good as the wizard AND those features as well. It creates a jagged progression (whereas I'm of the opinion that, while perfection is unattainable, good design should aim for as smooth a progression as is attainable).
So the Bard loses out on 2nd level wizard spell equivalents, right? Gets a cool thing equal to having 2nd level wizard spell equivalents. Then gets their next level of spellcasting and gets the same level equivalent as 3rd level wizard spells, maintaining the parity of their spell levels, but retaining the thing that they got in place of 2nd level wizard spells! What's the Wizard get?
2nd level spells.
The Bard misses out on total spell slots available, and relies on the ability they got instead of 2nd level casting to be equal to, not greater than, the wizard.
Additionally, this creates an issue with the spell levels themselves. There are already issues with the existing 1-9 spell level system, where some spells are too good and others aren't good enough for their spell level. A system with only 5 spell levels (meant to account for 20 character levels of progression) will undoubtedly have significantly greater issues with respect to such. I'd much rather see a spell level progression that paralleled character level progression.
That is a really good point. That spells aren't really that well balanced against each other, or even at their own level.
You'd need to spend time working out some kind of formula to make their costs similar. Which WotC either hasn't done or did poorly. But that's less an issue with this idea and more an issue of WotC's balancing metrics.
That said, I wouldn't be opposed to greater caster differentiation per se. However, I think this approach adds undue complexity without opening up much (if any) actual design space.
Disagree, but I'm interested in your ways of doing it!
If you want to differentiate the casters, then as I see it, there are two routes one could take.
The first would be to create entirely different casting systems for the different caster types. While this would undoubtedly add significant complexity, the resulting extra design space might be worth it (assuming it was done well).
Definitely interested. Honestly I think Warlock is the only caster who is remotely interesting in 5e because of their reduced spell slots recovered on a long rest and most of their exploration and social pillar casting shunted off into Invocations which creates this great dynamic of "Combat Magic" and "Noncombat Magic".
Honestly, if WotC embraced that they would certainly have an easier time of balancing spells in a given level...
The second would be to (for example) modify the casting classes to use the existing system in unique ways. For example, clerics might only be half casters, but could gain Thaumaturgy features that grant them the ability to perform miracles that the existing spells cannot accomplish (perhaps in this paradigm, healing spells are no longer spells, but rather a Thaumaturgy feature). This would also open up design space, while encapsulating added complexity within individual classes, but at the cost of less reuse of (high level) spells. Admittedly, if your goal is differentiation of casters, that's arguably a pro. However, in terms of effective use of page count, the less high level spells are shared, the less worthwhile it is having a lot of them in the rule book.
Making them Half-Casters just makes them Paladins, though. And Druids into Rangers.
Okay, you could argue that they'd have different class abilities separate from their martially-oriented counterparts, but take a look at your expansion of the Thaumaturgy cantrip to also function as Lay on Hands (In addition to healing it eventually gets status-effect removal and stuff, like higher level cleric magics)
It's a reference to the fact that Gary Gygax thought that 9 levels of spells was a good number for wizards to have. It's purely a legacy thing.
Huh! I did not know that. It's a good, solid, number, for certain! Evocative. Three and Three and Three for double layered mysticism.