To eliminate the problem of overheated neutral conductors, why not increase the size of the neutral?

First, increasing the neutral size does not eliminate the harmonic problem – they are still present in the system and may cause transformer overheating and possibly failure.

Second, installation of a new neutral conductor in long runs may be difficult and cost prohibitive when compared to the cost of installing an I-Trap™ unit.

What causes a neutral current to flow in a balanced three phase system?

The vector addition of three phase fundamental currents will add to zero on a balanced system without harmonics. However, if triplen* harmonic currents are present, they will add in the neutral.
With high concentrations of non-linear loads, the neutral current can be as high as two times the line current.

* Harmonics which are odd multiples of three (3rd, 9th, 15th, 21st, etc.). Odd triplen harmonics add together in the neutral conductor