Never buy a bunch of parts and expect a professional to install them.
Yup. I won't do it in my shop. Been there, done that. When the customer's parts fail, they expect me to eat the labor on their
parts I didn't make a nickel on. I suspect that is the root of the issue for shops that won't install parts supplied by the customer.
I have a local mechanic, plenty "professional" in my opinion, that does great work at a fair price and will put what I want installed on my vehicle whether he sold the part to me or not. He's the one that installed the South Bend clutch in my 98 dodge diesel, I ordered the clutch kit and he happily put it in. Maybe it's a big city issue but in my rural area the good shops will do what you ask within reason. There is one diesel shop that I have used a couple of times that always tries to push their preferred vendor's parts, but I try not to use them for that reason. If my favored mechanic wouldn't do what I wanted then I'd find another mechanic. Mine has made plenty of money off of me over the years. Just like with gunsmiths, if a mechanic doesn't want to do what I want done then I find another one. It's my money & my vehicle, so my rules.
