A plausible reason that the NEC does not permit conductors of different sizes to be placed in parallel because the current flow will not be safely divided between the different conductors. In the situation that you describe, using a 3/0 in parallel with two 350 kcmil conductors to carry 800A, the 350 kcmil conductors would carry more than their 'share' of the load.
When you have parallel conductors, the current divides up in proportion to the conductivity of the individual conductors. For conductors of the same length, the conductivity is proportional to the area. (Note: this is an approximation that ignores 'skin effect'; save that for another day.)
That 3/0 conductor has an area of about 168 kcmil. So if you put a 3/0 in parallel with a pair of 350 kcmil conductors, then the 3/0 will carry about 19.4% of the current, and the 350's will carry about 40.3% of the current. Take your '800A' figure and multiply it by those proportions. The 350's are left carrying more than 320A, the 3/0 is carrying less than 160A. The 800A breaker would not properly protect the parallel set of conductors.
-Jon