I'm not sure where to start. I don't want to tear the system down. But I want to tear a lot of subsystems out.
Simplified ability score modifiers as in BECMI but even simpler: 1-4 -2, 5-7 -1, 8-13 +0, 14-16 +1, 17-19 +2, 20-22 +3, etc. This make 18 less special and hopefully reduces stat dominance in the system. When you are only get at most +2 bonuses from stats they are no more influential that circumstance modifiers (per 3e). It also means you can have races with +1 stat bonuses. Hopefully it also encourages the 3d6 6-times style of chargen.
Strength modifies all damage (except machines like crossbows). Dex modifies all attack rolls. Con adds (never subtracts) to hit points. Int modifies all initiative rolls. Wisdom modifies all surprise checks. Charisma modifies spell resistance. Magic does not add to ability scores, it adds bonuses to ability score checks. Gauntlet of Ogre Power would be +2 to all strength checks and double your carrying capacity.
There are a fixed set of experience point progressions shared by various classes and multiclass gestalts. So a ftr-5 might have the same xp as a ftr/mu-3. As an example, 1-1000 xp might be base for swarthy-types, 1-1500 xp for fighters, 1-2000 xp mages and then ftr/thf might be 1-2500 xp and ftr/mu 1-3000 xp. Or something. Ultimately the numbers would work out that the multiclasses were about 1.5 levels behind the single classes. Triple-class would be optional and pin about 3 levels down from single classes.
Weapons are special effects. Each class has a damage rating by weapon size and level. At 1st level: Fighters would do d8 with large weapons, d6 with medium, d4 with small. Clerics would be d6/d6/d4, Thieves would be d4/d4/d6 (even a sap does d6). And mages would be d4/d4/d3. Fighters would progress at 4th, 7th, 10th and 13th levels. Clerics and thieves would progress at 6th and 11th levels. Mages would progress at 7th and 13th levels. GENERALLY. Specific classes might work differently. At 13th level Fighters might be 3d8/2d10/d12, clerics 2d6/d10/d6, thieves d8/d8/d12, mages might get to d8/d6/d4. Fighters would gain ONE additional attack at 8th level.
Individual weapons would have size and damage type (blunt, pierce, slash) and various armors would defend against weapon types differently. (Someone wrote about turning Armor Class back into armor classification above and I liked that idea. Switch it all to AC-A (humanoid flesh), AC-B (padded), AC-C (leather), AC-D (ring), AC-E (chain), AC-F (plate), AC-G (reptilian), AC-H (chitin), AC-I (rock), AC-J (extraplanar), etc.
Shields (like magic armor) provide a penalty to attack.
Combat: I'd have two combat systems. One simplified: 1d6 per side of the conflict. Everybody on each team goes before the next team goes. Roll Init each round.
The other system would be a fully segmented wargame like combat sequence. IMO, 3e and 4e abstract away too much of what makes a good wargame good: Simultaneous actions, segmented movement, etc. The important thing is that both systems are fully supported by the rules such that neither seems like an afterthought.
I would use the non-weapon proficiency system. But the NWP would not give you an ability others lack. It would just provide bonuses when you did these things. For example, anyone can swim but someone with Swim NWP gets a bonus to swim checks. I'm tempted to say the bonus is 1/2 level: something that scales with the character so that NWPs aren't obsoleted by magic (as easily).
Magic: My solution to the problem of magic getting powerful as you rise in level is to put off the speed of its rise. Mages and clerics gain access to new spell levels every 3rd level (at 1st, 4th, 7th) etc. Some monsters might have to be altered because certain spells would become available later but that's a balance issue that is easily fixed. Clerics would have prayer books, just like magic users have spell books and both are limited to casting spells in their spell books.
Not sure how I'd handle "saving throws". There are benefits to all 4 edition's takes on saving throws. Without spending a lot of time thinking about retooling all the spells too I'm going to leave this up in the air.
At this point, I'm thinking I'd rather be discussing a BECMI 4th edition (Holmes, red/blue B/E, and BECMI/RC being 1st, 2nd and 3rd). Though I'd split race from class immediately making it unlike BECMI right off the bat.