Artificer - delete it. Save it for the "Over-the-hill-wizard's Bucket of Ideas That Weren't Good Enough for the First Book" supplement.
Barbarian - delete it and make it a subclass of fighter
Bard - make it more like warlock than just "wizard that sings". I like the idea from OP of songs that you refresh from round to round, but I don't know if that's fun to play (waiting for your turn and then "i keep singing"). remove auto rapier proficiency, if you want the one perfect weapon for your not-really-martial character, you have to spend something to get it or live with simple weapons
Cleric - make being support fun instead of making cleric just another dps. if healing or damage prevention had some tactical space that would help, but the thing clerics are the best at (healing) is only a good strategy if your friend is dead.
Druid (and some others, like Find Familiar or Conjure Elemental) - remove all reliance on Challenge Rating. It's a bad system, and worse if it's player facing. Tasha's did this right for beastmaster ranger, and druid should get the same treatment. Also, delete druid and make it a subclass of cleric
Fighter - anyone can do what 5e Battlemasters can do, Battlemasters are just better at it. Tripping and Feinting aren't the sole property of the Battlemaster.
Monk - delete it and make it a subclass of fighter. Or just delete it. The class design is absolute crap, the subclasses hardly add anything to the base class, indicating that there's not enough interesting design space here to make it a full class with a variety of subclasses.
Paladin - tune down divine smite, or tune down divine smite crits. Make the smite spells useful.
Ranger - Spell-less by default. Some spell-like abilities, and a subclass that leans into spellcasting.
Rogue - Have a system for stealth/vision that isn't an adjudication headache. remove auto rapier proficiency, if you want the one perfect weapon for your not-really-martial character, you have to spend something to get it or live with simple weapons. Make sneak attack feel less generic. Put in more ways to earn sneak attack through smart play, and remove the absolutely mindless "my friend is nearby" trigger we have now.
Sorcerer - delete it and make it a subclass of wizard, or actually make them distinct. Wizard and Warlock are distinct, sorcerer is like a naughty word version of wizard with a little warlock flavor.
Warlock - kill eldritch blast, make all available shooty shoot cantrips work as split rays based on warlock level (not character level). Be int-based. Do something else with their spell slots, but 2 per short rest feels bad. Lower the level 1-3 power and raise the 6-20 power so they're not just a dip.
Wizard - you've got 8 nearly identical subclasses in the PHB. It doesn't really matter what kind of wizard you are, at the end of your day your fireballs still do 8d6 damage. That's a waste of pages. Make that specialty choice matter. Boost spells of your school and nerf spells of the other schools, maybe something like "spells of your specialty school are upcast one level for free; spells not of your specialty school do not benefit from upcasting".
Help DMs actually make player decisions have ramifications rather than handwaving everything and letting the game design burden fall on DMs. Looking at you, warlock-paladins, but every class should actually pay a price for multiclassing. Giving up worthless capstones is not a price.
Half-casters have to go. Nth level pal/rgr spells are designed with the knowledge that you get them when wizards are getting 2Nth level spells, so sometimes they are stronger than other Nth level spells. Then, some intern 6 years later thinks "here's a healing spell clerics don't have? well, let's make that available to clerics" without thinking about the reason it's exclusive to pal/rgr and somehow it gets published!
Make all classes MAD. Martials in 5e at least have to decide between Stat1 that increases their melee damage and Stat2 that increases their melee damage and ranged damage and AC and initiative and several useful skills. Full casters each have one stat that matters, then CON and DEX as desired, dump the rest. Make each mental stat have a value for martials, and they choose which one of those 3 they can afford to focus on. Make CON not universally the second best stat. Nerf DEX.