True, but when the damage just expands in a linear fashion, it loses a lot of it's appeal. I picked a two round duration because it illustrated the point, and it ceases to compound damage after the second round of casting. But when every additional combat round just deals the same volume of damage...
Granted, you could Residual Metamagic it into additional applications, bouncing which was rod-boosted and which was Residual boosted in a 2 out of 3 loop, but it's not quite the same, and pretty limited in per day ability, then.
First, you are completely correct, this is close to be not a viable sorcerer build unless you want to copy black mage. It has nothing of note, and dealing more than 2k damage in one round makes no sense anyway. This build can only do all this once per day, after wards it has to cope with being a regular sorcerer of about 15th level worth of spells. Where all his spells are probably either quickened, repeating or twinned (at +1 level each). However, apart from that the build has nothing to offer that a regular sorcerer build can't do, so it will get outmatched by most wizards that know shield or invisibility or both. Taking damage will neuter it totally. I'm in no ways attempting to post a viably build, I'm just trying to pump out as much damage with magic missile as possible.
Second, Due to the manner of Repeating spells inside repeating spells inside repeating spells, the Build would dish out most damage if it did it in round 4 or 5. However, I don't think there are spells for that.
Third, I edited the post to account for the energy admixture mistakes, and also to account for choker having extra actions.
Fourth, can we find a way to add more actions? This is the only thing we need now. With Level 9 spells at our hands one should think there'd be a possibility with all those spells we can get our hands on.