Many years ago I bought a secondhand engine from a reputable seller and got a local garage to fit it in my car.
The seller provider a warranty for the engine. The garage warranted their work.
After fitting the engine, it turned-out that it was knocking. The engine supplier agreed to replace it with another engine, under their warranty scheme. I had, however, to pay the garage again for the labour.
Had I asked the garage to supply and fit the secondhand engine, I wouldn't have had to pay for the labour twice.
I am not suggesting that you should never supply your own parts, I still do sometimes (and I am aware I am taking a risk), just that when you do, you should keep in mind that if the part is defective then you will likely to have to pay for the labour again.
As for MarkPortugal's point, this hasn't actually happened to me yet, but it is of course another risk involved in getting the garage to fit parts you supply - i.e. a dispute on whether the part is faulty, or wasn't fitted correctly. And another potential issue is if the part supplier claims that the part was damaged due to incorrect installation.