Just search for "XXX lost my booking" on FT and you will find the hundreds of horror stories about just how badly things can go wrong when you have not booked directly through the carrier.

It would have to be a very substantial savings and a very simple routing before I would even think about using anything other than the carrier or a reputable TA (not a website).

When things go right, it doesn't matter. When things go wrong, they go really wrong and you can sue evereybody in sight after the fact, but you will have that horrible view of an aircraft, your aircraft, pushing back from the gate while you're sitting at the gate.