A few things:

I am not aware of any brand that offers additional discounts for being exclusive. Generally, they offer lower dealer pricing when you buy X amount of product for your annual stocking order, regardless of whatever else you carry. However, this usually entails them wanting you to stock X amount of house product as well, such as Bontrager fro Trek dealers and Pearl Izumi for Shimano dealers now that they are direct only.

Specialized is the only company to my knowledge that really, REALLY tries to push other product out of their dealer's shops. The company I work for dropped Specialized a few years back for this very reason. At the moment, we carry Trek, Electra (now Trek owned) Cannondale, Salsa, BMC and Colnago. We previously carried Scott, which is what Specialized had issue with, even though we were selling a ton of bikes for them.

I've very rarely seen shops that are exclusive to one brand. Mostly for the reasons listed. It's better to have more than one option for the same range. Looking for comfort? I can show a customer a Domane, Synapse and Grand Fondo in one day.

I'll not pretend to know the specifics of exclusive shops because I've never worked for one, but occasionally, we will get a bike from a manufacturer that is "on loan" where we don't pay for it unless we sell it (I can get you a sweet deal on a first gen Impec). Perhaps this happens in one form or another at some of these exclusive shops.