Reducing the Impact of Ability Scores

I have no idea what prompted this, but what if ability score modifiers in D&D were handled in four-point bands instead of two-point bands?

That is, instead of

Score	Modifier
1	-5
2..3	-4
4..5	-3
6..7	-2
8..9	-1
10..11	+0
12..13	+1
14..15	+2
16..17	+3
18..19	+4
20..21	+5

you have

Score	Modifier
1..4	-2
5..8	-1
9..12	+0
13..16	+1
17..20	+2
21..24	+3

I’m wondering what might make this a bad change.  It reduces the impact of ability scores, but that’s the point of doing this.

Generally on opposed checks (attack versus Armor Class, spells versus saving throws) the changes will reduce the impact on die rolls.  I’ve become comfortable with the idea of Falling off the RNG, but I’m quite comfortable with that not happening, too.  Where two roughly-equal characters (both with high ability scores, or both with low scores) square off there is no net change, but larger differences in ability scores can be accommodated less painfully. A high-Int character (now capped at perhaps 23 if there are no enhancement bonuses, as described below) has a +3 modifier against his Dex 10 target’s +0.  Even with a poor Reflex save, a ninth-level spell (save DC = 10 + 9 + 3 = 22) might actually be savable (d20+6+0 = 22 on a 16) 25% of the time.

Enhancement bonuses perhaps get strange, since it now takes four points difference to ensure a measurable (i.e. ‘to the modifier’) change.  I don’t plan to have enhancement bonuses (as described in Magic Item Complaints and Corrections) so enhancement bonuses are not an issue for me.

Racial modifiers are in the same situation, needing four points to ensure a measurable difference.  I’d rather have qualitative racial differences than quantitative differences.  That is, rather than say “orcs are strong” and give them a +4 bonus to Strength, simply give them abilities that work better with high Strength and let the character designers take care of the distinction themselves.  Players and DMs tend to like to reinforce the good abilities, so I think in this scenario you would be unlikely to find Orcs with Strength lower than 13.  On average much stronger than average humans, without needing to be similarly stronger than the strongest humans.  This also removes the need for orcs to be stupid — you might find the occasional really smart one, but since most of them would be strong rather than smart (due to the bias just mentioned, and generating ability scores on something like a point-buy system) you could expect them to generally happen anyway.  If being an orc rewards Strength- and Constitution-based builds you can expect to see orcs built around those abilities and shorting the other ones.  This might also help fix the idea of favored classes — orcish racial abilities suit fighters and barbarians well, wizards and perhaps paladins not so well.  I think overall you could expect to see characters fitting racial archetypes more often than not.

If bonus spells are based on modifier rather than base score (which I would be inclined to do as well), it might help curb caster overpower.  Not a bad thing.

It would reduce hit points overall and make the Hit Die more important in hit point calculations.  This is probably a good thing

It occurs to me that 18 might no longer be functionally the best result possible for a beginning character, since 17 and 18 both have the same overall effect.  I do feel this one a little, but it’s more of a nostalgia thing I think.

Are there any other concerns I should address or consider here?  I’m seeing mostly good things come out of this.