This whole thread is basically "fantasy heartbreaker" thinking in detail.
There's no actual design
problem being solved, which is evident from the first post. There's an opinion from some that "things should be different", which is not the same thing at all. The OP proposes a basically different design for Bards, and one unlike any other class in 5E - that of being forced into a support role with no other choices. Clerics aren't like that, Druids aren't like that. No class is. Because D&D 5E doesn't do forced support roles. 4E did - it had cleanly separated roles, and a support Bard worked well there because 4E had stuff which made support classes extremely strong and fun to play - something 5E is profoundly missing.
What's also funny is that, by following the OP's suggestions, the Bard would be an
extremely bad support class. By having a vastly smaller number of spells, and being limited to slowly acquiring level 1-5 spells, the Bard would be hugely inferior in performing support to Clerics/Druids and so on. The OP doesn't seem to have taken on board that in 5E, most support functionality has been moved back to spells. And just adding to the "fantasy heartbreaker" vibe, what are the OP's suggestions for specializing/differentiating Bard subclasses? Spells. They're all spells. Some of them are spells which the Bard wouldn't even gain access to until what, level 17? Like, seriously, you want not only to give Bards a much smaller number of spells, and much weaker spellcasting, but you also want to limit them further with a theme? Just wild. As bonus to that, many of the suggested spells are terrible spells mechanically - weak, ineffective or niche spells which are not fun to use.
And suggestions like this:
I also think the druid should ALSO be a half caster. The difference between Nature domain clerics and druids is already ridiculously tiny from a conceptual perspective, druids should be focused on their class-unique mechanic (wildshape). They should still get cantrips though.
Pure fantasy heartbreaker thinking. The classic "Yeah I know it's been a full caster for many decades, but like, I think we should theme entirely it over this one ability which, in literary fantasy and mythology, isn't even a primary druid thing, because that's my opinion!". And we apparently don't even consider whether the real problem is nature domain Clerics being a thing (hint: it is), rather than vice-versa.
Let me just add - I think a lot of this thinking comes primarily from older video games. Bards being a purely supportive deal is completely an early MMO thing (it's not even true of modern MMOs). Druids being all about shapeshifting is primarily something seen in video games (particularly World of Warcraft). But in those games they at least got incredibly impressive abilities that no-one else had access to, and unique mechanics to support them. Here we're just looking at them being a bad caster who has some weak support abilities, rather than a custom-designed class with its own mechanics. Which won't even impress people if they somehow time-travelled from 2000 and wanted to play a support-only Bard.
On top of all this, the idea that the Bard "needs changing" is utterly repudiated by the fact that 5E Bards are incredibly popular. And they're not played the way the OP wants them to be limited to being played. This really destroys the idea that there's a "problem" to be "solved" with Bards as class.
There is, I'd argue, an actual issue with 5E that the OP and others don't fully seem to appreciate, which is that a lot of people want to play a Spellblade or Red Mage or similar class, and 5E is godawful at providing such a class, and definitely some people playing Bards are doing so because it's one of the less-awful ways to do that. But you don't fix that by weirdly limiting Bards to a role no other class is limited to (not even Artificer). You fix that by providing a Spellblade class.
