[daughart]

As for your first point, shotgun sequencing was not invented by Illumina. Shotgun sequencing, or sequencing many small fragments and then computationally reconstructing a larger contig, was first done in 1979, and later used by many groups (most famously by Celera Genomics in their quest to beat the human genome project). Shotgun sequencing can be done using any short sequencing reads, so this is neither a breakthrough nor even an advantage for Illumina.

Illumina's chemistry was better than the others, and they marketed their advantages better. The Illumina machine produced longer reads than SOLiD (Life Technologies), and produced more reads than 454 (Roche). They produced reliable instruments that were relatively easier to use than the others also, which made them favorites for core facilities.