I can immediate think of two reasons why basic training should not be divided based on MOS. 1.) By mixing those who fight and those who support there might be a more urgent understanding of the needs of those who fight by those who support. 2.) You never know when you might have to fight, even when you support. Afterall, the Pentagon was attacked on 9/11. While there wasn't an opportunity to fight back on 9/11, I would certainly hope that if the opportunity presented itself to kill Muslim bastards on the streets of America that our soliders would be prepared to do so.
I can tell from personal experience. The 1st time I joined the Army I went to the old basic training of 8 weeks in 1969, and then 11B Infantry Advanced Individual Training for another 8 weeks. A lot of the training just repeated what was already taught in Basic. It was good for about 3 - 4 weeks of extra PT.
I rejoined the Army in 1980. I had to do OSUT for 11C, but all the 11B, 11C and 11H folks in the company finished training in 13 weeks.