Ability scores also make half-feats viable. It may not seem like an explicitly stated rule, but it does have effects and consequences. Many a character has chosen a half-feat when they have an odd score. But it has consequences even when a character intends to take two half-feats in a row, which you couldn't get if there were only the bonuses. Because after the first feat, there's another four levels where they are not yet benefitting from their score increase. That's part of the price their character pays for those feats, and is the reason that two half-feats are not exactly the same power-level as one regular feat and one ASI.
It's also common for a point-buy character to put a 13 in a secondary score, fully intending to raise it to 14 at level 4 with a half-feat. This allows him to avoid two points of point-buy for the 14 (see point-buy rules), but the cost is that he doesn't really benefit from that investment during levels 1-3. If there weren't scores in addition to bonuses, this sort of fiddliness would be removed from character creation. Some players are always glad to simplify things, but some players would miss it.