Minimalist D&D XIII - skill use, proficiency all the time, or no proficiency at all

As you might know, I'm trying to reduce the number of skills in 5e; skills are one of my least favorite parts of the game.

One thing I dislike is how some skills are practically useless while others are ubiquitous. The user Merudo has compiled a couple of lists that illustrate this point:

I've searched through the adventure Waterdeep: Dragon Heist and counted the number of times that a given skill is used in an ability check.

Here are my results:

• Athletics: 48
• Acrobatics: 6
• Sleight of Hand: 3
• Stealth: 9
• Arcana: 6
• Investigation: 15
• History: 3
• Nature: 3
• Religion: 4
• Animal Handling: 3
• Insight: 10
• Medicine: 0
• Perception: 56
• Survival: 3
• Deception: 9
• Intimidation: 16
• Performance: 1
• Persuasion: 22

So the main skills are Perception (56), Athletics (48), Persuasion (22), Intimidation (16), and Investigation (15).

Note that some of these skills will actually show up more often than listed in the book, simply because the checks are a result of player actions. That's especially the case for social skills, Stealth, and Sleigh of Hand.

 

I've searched through the adventure Tomb of Annihilation and counted the number of times that a given skill is used in an ability check.

Here are my results:

• Athletics: 51
• Acrobatics: 14
• Sleight of Hand: 1
• Stealth: 10, plus extra opportunities if moving at slow pace
• Arcana: 5
• Investigation: 10
• History: 4
• Nature: 2 + recognize 8 plants/animals
• Religion: 6
• Animal Handling: 4 + dinosaur race
• Insight: 2
• Medicine: 4
• Perception: 96
• Survival: 13 + navigation checks
• Deception: 8
• Intimidation: 3
• Performance: 1
• Persuasion: 11

My initial idea was consolidating the skills in a few skill sets, but I'm this close to just giving everyone proficiency in everything. 

I'm half convinced it won't break the game, and it will make things a lot easier. I didn't like this in 4e - a high-level wizard going from +0 to +15 in athletics felt like too much - but +2 to +6? Well, why not, Gandalf can jump over that chasm after all.

That level 20th fighter? Yes, he DOES know a thing or two about arcana. He cannot cast spells, but he has seem plenty of sorcerers, spells, monsters and magic weapons.

And, of course, every adventurer becomes better at saving throws.

Robson Michel - source.

So, giving everyone proficiency would take care of that. If you need a specialist, he would get expertise instead.

On the other hand, I also considered ditching proficiency entirely in favor of ability scores.

If I do that, I'd still want saves and "skills" to raise with time. Maybe I should go the 4e route and just give +1 to everything at level 5, 11 and 17. A level 20 wizard with Strength 11 to 13 sounds ok to me, an even Conan shows above average intelligence as he progresses.