Yes, I agree Teach First isn't perfect and is very well marketed but compared to a lot graduates coming off training courses, (a lot of unis have under subscribed BEds or PGCEs), they do have an edge.
It is not that they bring their better subject knowledge, but they are prepared to listen and take on advise, put in a lot of commitment and tailor their teaching to the fact they are in a deprived area.
The teach firsters I have met have all been primary and two stuck out. They had done education or child psych/childhood studies related undergrad degrees and all were highly committed and knowledgeable about working with children. Some of them saw teaching as their long term plan and had big ambitions. They made fab teachers. It is the (few) with the stereotypical attitude that it will launch them into the city jobs and be a fun start to their career that struggle, but I have seen Teach First filter them out. Friends DC who have applied who are arrogant, clearly not in it for the teaching/mission and not at all equipped for teaching, do not get a place.
Also, one final point(!) TF DO train their teachers a huge amount before putting them in the classroom. DDs best friend did a large number of essays and school experience time before the Summer Training, then 6 weeks of the residential summer training which was a lot of the content of a PGCE, with essays and tasks to do during the summer. Then when she started she was heavily supported, off on training evenings, weekends and days, and in the holidays had weeks of training.
Not saying it is at all perfect, but neither are the other routes.