###There are already rules for using double weapons as regular two-handed weapons

The weapon’s base damage di(c)e don’t change, but you get the 1½ Str to damage and the increased returns from Power Attack.

Between those advantages, and the very high number of feats necessary for TWF, the consensus is actually that this is the optimal way to use double weapons (which, effectively, means that you should never use an exotic double weapon since you shouldn’t be using its double status anyway, which means you should save yourself the feat).

Thus, the weapons do not need a base-damage bonus for this use. Double weapons as a pair of weapons are weak enough as it is.

###Strict RAW, though... you actually get those benefits while using both ends

Double: You can use a double weapon to fight as if fighting with two weapons, but if you do, you incur all the normal attack penalties associated with fighting with two weapons, just as if you were using a one-handed weapon and a light weapon.

(emphasis mine)

Double weapons may be used as with two weapons, and when you do so you get the attack penalties of fighting with a one-handed and light weapon. It doesn’t make the double weapon, or either end of it, one-handed or light for any other purpose – including damage. And the double weapon is, after all, still being wielded with both hands. Thus, strict-RAW, you get 1½ Str to damage and increased returns on Power Attack even while using both ends.

This ultimately doesn’t usually matter that much; the TWF feats require a ton of Dexterity so it’s hard to pump your Strength enough to overcome, say, Sneak Attack damage. The one case where it makes a big difference is the TWF ranger, who gets the feats without needing to meet the requirements: thus the ranger can actually take advantage of this bonus by pumping his strength.

It’s still a very feat-intensive tactic with less than stellar results, though. It’s almost certainly unintended, I’ve never met a DM who played it that way (excepting those to whom I specifically brought this up, several of whom were willing to allow it), and it runs counter to most people’s intuition. In D&D 3.5 (which actually had different text but it worked out the same), there was even a prestige class that gave this effect as its capstone benefit, giving pretty strong suggestion that it wasn’t intended as the default.

But it does, finally, give an actual purpose to double weapons: it’s not a great use-case but at least there is some situation where someone optimization-conscious might actually want to use Exotic Weapon Proficiency for a double weapon

###Easier houserule: just make up a new free weapon

Give it the stats you want, call it a separate weapon. Far fewer side-effects than changing how every double weapon ever works.

There are already rules for using double weapons as regular two-handed weapons

The weapon’s base damage di(c)e don’t change, but you get the 1½ Str to damage and the increased returns from Power Attack.

Between those advantages, and the very high number of feats necessary for TWF, the consensus is actually that this is the optimal way to use double weapons (which, effectively, means that you should never use an exotic double weapon since you shouldn’t be using its double status anyway, which means you should save yourself the feat).

Thus, the weapons do not need a base-damage bonus for this use. Double weapons as a pair of weapons are weak enough as it is.

Strict RAW, though... you actually get those benefits while using both ends

Double: You can use a double weapon to fight as if fighting with two weapons, but if you do, you incur all the normal attack penalties associated with fighting with two weapons, just as if you were using a one-handed weapon and a light weapon.

(emphasis mine)

Double weapons may be used as with two weapons, and when you do so you get the attack penalties of fighting with a one-handed and light weapon. It doesn’t make the double weapon, or either end of it, one-handed or light for any other purpose – including damage. And the double weapon is, after all, still being wielded with both hands. Thus, strict-RAW, you get 1½ Str to damage and increased returns on Power Attack even while using both ends.

This ultimately doesn’t usually matter that much; the TWF feats require a ton of Dexterity so it’s hard to pump your Strength enough to overcome, say, Sneak Attack damage. The one case where it makes a big difference is the TWF ranger, who gets the feats without needing to meet the requirements: thus the ranger can actually take advantage of this bonus by pumping his strength.

It’s still a very feat-intensive tactic with less than stellar results, though. It’s almost certainly unintended, I’ve never met a DM who played it that way (excepting those to whom I specifically brought this up, several of whom were willing to allow it), and it runs counter to most people’s intuition. In D&D 3.5 (which actually had different text but it worked out the same), there was even a prestige class that gave this effect as its capstone benefit, giving pretty strong suggestion that it wasn’t intended as the default.

But it does, finally, give an actual purpose to double weapons: it’s not a great use-case but at least there is some situation where someone optimization-conscious might actually want to use Exotic Weapon Proficiency for a double weapon

Easier houserule: just make up a new free weapon

Give it the stats you want, call it a separate weapon. Far fewer side-effects than changing how every double weapon ever works.