I don't want to remove Intelligence, I want it to be more useful. But that's not what this thread is about.
If I did want to remove Intelligence, I would probably remove all of the ability scores, and rework them into six new stats.
Physical: a combination of Strength, Dexterity, and Constitution.
Mental: a combination of Intelligence, Wisdom, and Charisma
Magical: a measure of one's affinity to magic, the supernatural, and the paranormal
Power: a measure of your character's ability to affect others in some way
Defense: a measure of your character's ability to resist others in some way
Luck: a measure of your character's good fortune.
Each stat is a number between 1 and 6. You "build" your character by distributing 21 points among those six stats however you like. A stereotypical "warrior" character would have 6 for Power and Physical, and 1s for Mental and Magical, for example.
All rolls and checks in the game would be made from a combination of 1d20 and two of these modifiers, and use opposed rolls (or a fixed DC, if there is no opponent around to make the check against). The highest result wins, ties are rerolled.
- To make a weapon attack, you would roll (1d20 + Physical + Power) and your target would roll (1d20 + Physical + Defense.)
- To make a spell attack, you would roll (1d20 + Magical + Power) and your target(s) would roll (1d20 + Magical + Defense).
- To convince a merchant to give you a bargain, you would roll (1d20 + Mental + Power), and the merchant would roll (1d20 + Mental + Defense.)
- To find a hidden switch in a bookshelf: roll 1d20 + Mental + Luck vs. DC X
- To avoid a fireball trap: roll 1d20 + Magic + Luck vs. DC X
I realize that by this point, we are no longer playing Dungeons & Dragons...we are playing a completely different RPG with vastly different dice mechanics. But that's what I think it would take to remove Intelligence (or any other ability score) from the game.