A few comments on this subject…
One that I’ve heard from a long time famous Berkeley BMW shop owner, recently retired. And I’m paraphrasing here… “Would you bring your own steak to a restaurant to have the chef cook it for you? I think not.”
Now, I do know of restaurants connected with fishing boats that will cook what you catch. But that’s very special circumstances.
As for specialist repair shops, and I’ve been involved in the industry one way or another my entire life. All repair shops have a ton of overhead, in the rent, waste oil removal, labor, etc., and making money on parts is actually a BIG part of their business. Most shops that work on daily driver modern cars like to source parts from their own suppliers. Even though many customers have access to look up and buy parts off the internet for sometimes less than the shop can even get them for from their regular suppliers. That doesn’t mean the shop is gonna go all over shopping for the best price. They have a good relationship with their suppliers, and that includes whatever warranty comes with those parts, and the brand knowledge too. A shop just can’t keep track of where they got every part if they have to shop all over for best price. It’s too much effort to figure out who’s gonna warranty what.
Lets say you have a shop do the regular thing and supply all the parts for a given job. They warranty all those parts, and their labor to replace the part if it fails within the warranty period. When you supply said parts, the shop doesn’t have to warranty their labor, unless it’s an error of installation. Meaning, if you supply a part, the shop installs it, and it fails, you have to pay all the labor to have them replace it again.
That’s for modern cars, and easily accessible parts. As for older cars that sometimes need parts to be sourced from alternative places, and sometimes from all over the world. Some of those parts have no warranty. Either because they’re used, NOS, or whatever. Some shops have been doing the old car thing and have a number of connections they can call on to source parts, others don’t. Sometimes the customer has a different connection than the shop and can source something that the shop either can’t or would take labor time to call all over… Part of sourcing old car parts is the time it takes to track them down, and that costs money too. Costs them money, which costs you that money.
It all comes down to your relationship with a given shop and the ease of sourcing parts for whatever year of car.