What I wrote posted:

Ability scores affect eight areas of Dungeons & Dragons:
• Basic attacks, which are based off strength and dexterity for melee and ranged attacks, respectively.
• Initiative, which gains a bonus equal to your defence modifier.
• Hit Points and Healing Surges, the first taking your constitution score, the second taking your constitution modifier.
• Attacks and Damage, which use a particular modifier based on a primary attribute, and may have various other affects based off of a secondary attribute.
• Defences, in which you gain bonuses based upon the highest score of a particular pairing. (FORT: STR/CON, REF: DEX/INT, WILL: WIS/CHA)
• Skills, where each skill uses an attribute as a modifier to rolls. (eg: a character with 12 STR (+1) gets a +1 bonus to Athletics. a character with 12 DEX gets a +1 bonus to acrobatics, stealth and thievery.)

If you wish to do away with ability scores, these areas will have to be reworked.

When People say death to ability scores, what they mean is 'as a character, ability scores affect both combat and out-of-combat encounters. This means that I am hamstrung from certain noncombat encounters by my reliance on ability scores for combat mathematics.'

The second reason to get rid of them is that they put a layer of abstraction between the real numbers and the players. There is only one instance in which you use the actual attribute value: when calculating hit points. In all other instances, you use the modifier.

And finally, once these areas are made independent of ability scores, they serve no purpose. they do not differentiate. they are simply numbers on a sheet, with no real consequence in their raising or lowering.