I'm curious as to how you would fix all those "problems" while still making use of any 5e game material. Including the core books.
Attributes
Stats
Traits
Qualities: These are minor powers, such as Healing Factor, Danger Sense, Regeneration etc.
Talents: Partial powers
Edges
Skills
Specialisations
Stats-
Strength, Endurance, Dexterity (Reflexes), Willpower
So for each strength level I would assign a comic book levels, or tiers, e.g. Athletic, Olympic, Peak; to which I would add in Paragon, Enhanced, and Superhuman, with various levels. Not only that, Str 20 would be lifting approximately 16,000 lbs, double that on a passed test. Same would go for Endurance, such that at each tier their healing would improve; same to with Dexterity, and Willpower being able to resist mental abilities. So in between these tiers, the lifting capacity may increase slightly for example. So if a monk or fighter has no powers, or magic - well look at the badass Batman is. This allows an easy way to gauge players abilities.
Edges / Feats-
These need splitting, like with Savage Worlds such that it allows totally bespoke class creation.
Traits: These are minor things like Fleet of Foot (adds 5 mph each time you purchase it). So we can do away with this Fast Movement nonsense, as this gives a clear speed benefit. So a barbarian could easily run as fast as a horse if they wanted to get it. It would also cover individual languages, or things like Ambidextrous, Alertness that kind of thing.
Combat: Could be split, similar to Pathfinder, and Palladium stuff, into Weapon Groups (Weapon Proficiency), Assassin, Martial Arts, Pankration, Weapon (weapon specialisation). These would be similar to both Savage Worlds, 5e, 13th Age, Modern Age; and be split into say Martial Arts I, Martial Arts II and Martial Arts III. Each would confer a bonus, like any other feat, during combat.
Background: This is obvious
Ancestry / Lineage: Also obvious, but just in case, elf, dwarf, dragonborn etc.
Class / Profession / Occupation: Knight, Monk, Martial etc.
Magic: This would detail the type of magic, whether Artificer, Arcane, Pact, Innate, Divine and what have you. There would also be another, and let's take a lead from Savage Pathfinder, Mystic Powers.
Mystic Powers would cover a monk's, or Paladins class abilities. For martial type abilities I would steal some of the names and principles from Gurps Martial Arts, and from Runequest for these, as well as the various DnD books from previous and current editions.
Powered: Types of magic, e.g Cantrips, Spells, Circles (mentioned later).
Tier: Which tier you are. Basic, Intermediate, Heroic, Legendary, Epic
Skills-
Athletics, Arcana, Computer, Computer, Craft, Espionage, History, knowledge, Medicine, Nature, Pilot, Science, Survival, Technology
Specialisations: This would cover individual proficiencies.
Spells
DnD like Runequest has a spell spam problem, but not too hard to fix.
I would import from Savage Worlds the basic spell types, Barrier, Protection (Mystic Armour), Blast, Bolt etc, and add in Trappings. Then import the principles of Manipulation / Shaping from Runequest / Mythras individual spells to allow personalisation, e.g. fire, water, area of effect, extending the distance etc. Then all of a sudden you an easy way to create new spells.
Circles: This is an area of magic, e.g. Clockwork, Fire, Ice. You can remove individual spells, and this would only use the Shaping Mechanic.
Armour Class: Now this is a toughie to remove, but it absolutely needs to go in some ways - although it does speed it combat; whereas in say Palladium game can grind to halt and take hours. Now I get this can happen with 5e sometimes, but it does not need to. I haven't solved this one....yet. But I will.
Dragons
They like in Palladium, need some serious depowering, as they make no sense and should rule most worlds. But they don't. Now, it would be better if each plane maybe had different types, and sizes of dragons. So one plane could have say dragon riders, such that they are only bus sized. But another plane, e.g. Spaceships and Starwyrms may have spaceship sized; while another may have dragons larger than mountains, and could challenge a World Soul Primordial. Perhaps they could be primordials, or monster versions (Kaiju) like from Pacific Rim and Godzilla films.
Higher Level Games
Qualities: These would usually cover monster abilities, but also feature when you want to advance and use Legendary and Epic games. These are low level super powers, but also allow various sources: Biology, Magic, Superpower, Technology, Other
Levels-
1: The ability is minor and usually doesn’t affect another (sonar, infrared vision, etc.)
2: The ability is significant and has a minor effect on someone else (paralyzing venom, water breathing, etc.)
4: The ability is major and can have significant effects (intangible, invisible, etc.)
Talents-
These are partial abilities, and should only be at higher levels and would cover things like astral projection, demi-plane creation. For good examples of these I would look to Spheres of Power and use talents from there.
Cosmology
Version 1-
Personally, I would steal from Magic the Gathering here, such that each plane has a World Soul, and as such Primordials, Elder Evils, titans Gods etc can all be very different. Now the gods, generally, should be like those from the newer version of Clash / Wrath of the Titans. They can steal souls, and can also die and end up in the Afterlife. They can be split into Divine and Infernal.
Then have Astral Plane where the Aeons reside.
Old gods: They can be split into elder gods, and old ones. I would certainly steal from Midgard, in that they have faces and facades, such that they can take on the form of other deities if they chose. Each one may have a realm.
Eternals (Mystara Immortals): There could also be individual realms for and also have realms.
Then have a Cosmic Plane where those that rule, and watch the afterlife reside.
Now if I was to have a space setting, it would likely be its own plane, likely galaxy or maybe a cluster of galaxies in size, whereas most other planes would usually be solar system sized.
So if you wanted a kind of Spelljammer game, you could import this too.
Version 2-
Have separate God Planes, whether Angel, Demon, or whatever. Then in the middle, and connecting to them all have Sigil, a place where they can all meet in peace, similar to Marvel / MCU Omnipotence City.
Infinite Stair is a way to connect all the normal planes, allowing travel between them.
Then add in the Cosmics again, and you're all set.