Ok, here's something a bit more crazy:
First of all, assume that stat modifiers are stat-10. That's right, a 10 is +0, a 14 is +4, and an 18 is +8. This spreads ability modifiers twice as wide as standard d20. An 18 is the equivalent of a 26.
Now, with that kind of big spread, you want to make sure that 14-16 is a normal starting stat for attack, with 18 a lucky exception.
Rolling stats
* roll stats, 4d6 drop lowest as the default (average roll: 12.25)
* option to reroll if total bonus is under +3 or no score is 14 or higher
* race gives +1 to one stat; If already
17, add to other stat under 17
* class gives +1 to one stat; If already
17, add to other stat under 17
* feats to make melee attacks with any stat: Weapon Finess (Dex), Titan Style (Con), Tactical Duelist (Int), Mystic Martial Arts (Wis), Champion Style (Cha)
Effect:
* everyone has at least a 14, or 16 if race + class align perfectly
* There is only one way to get an 18: roll it. This will make an 18 fairly rare: 21/6^4 = 1.62% per roll, or 9,34% on 6 rolls
* A minimum 14 is pretty likely (over 40% per roll)
https://klubkev.org/~ksulliva/ralph/dnd-stats.html
Point buy
Distribute 15 points
score cost
15 7
14 5
13 3
12 2
11 1
10 0
9 -1
8 -2
7 -3
Player choice
Players can choose between point buy and rolling. The rules encourage the DM to be strict with begging for rerolls.
There is a clear benefit to either: With point buy, you can achieve slightly better scores than the roll average (12.25), and a more balanced character. However, without the downside risk of a really bad score, you also don't get the upside of a possible 18. The best you can do with point buy is a 17 with perfectly aligned race and class. If you want an 18, you have to roll. The 18 is reserved for the less than 10% lucky few.
Advancement
PCs get a stat bump every 5 levels. However, you can only raise a stat if it is equal to 10 + 1/2 level + race + class bonus or lower. The same limit applies to all other stat boosters, like Gauntlets of Ogre Power. This will protect the uniqueness of the 18 until level 10.