Many repair shops use BG products because BG will provide free equipment. When the Ford dealership I was at first started using BG they brought in a driveline service machine, two transmission fluid exchange machines, two coolant exchange machines, two induction service machines and a diesel induction machine. Provided for free, maintained by BG and replaced with upgraded models as available as long as we used their products.
The BG fluids were more expensive than Motorcraft but carried a higher profit margin.
My opinion is that their fluids are just fine. I prefer their gear lubes to Motorcraft as it’s been proven to just be an adequate fluid nothing special. Most of their additives are a waste of time and money. Their recommended schedule is insane(basically every fluid every 30k) and their warranty is mostly a gimmick due to having to follow their schedule for it to be valid.
It seems to be that the BG products are more marketed towards vehicles that have been abused and mistreated. If somebody was terribly concerned about trying to clean up their engine then they should use something like hpl, Red line, amsoil, etc. The only product I will continue to use with them is going to be 303 CVT additive. I had a ever so slight seat by a seal that's been known to act up on these cars and the BG product has kept it from leaking and kept the seals soft and pliable again. I've been very content lately we're just running mobil one and topping off as needed. But if I had an old junker I might consider using the epr from BG but probably at half the dosage. Most cars that have ran a good quality synthetic and had it changed regularly may not see any benefits for the BG. If you would at least follow the manufacturer suggestion on changing transmission fluid, coolant, and brake fluid I'm sure you'll be fine
Dealerships don’t care. As @cb_13 pointed out, BG provided equipment for free and their products are priced in a way that provides a significant amount of profit margin for the service department. In case of a failure, the dealership will still submit for factory warranty but even if, in the exceptionally rare occurrence, it gets rejected, BG offers the dealership extended warranties on their products. The dealership looks at it as a win-win, and it really is for them.
BG products are just fine. I don’t think they’re anything special, but there’s nothing wrong with them, either. I wouldn’t be upset about their use in my car, but that’s just me. I understand why someone would be upset if a dealer used BG fluids when they thought they were paying for OE.