No matter what you do you're going to need the functionality of a preamp. Which means that the sound of your system will be affected by the preamp in an integrated, in a DAC with preamp, streamer, or whatever you use. I have used my headphone amp as a preamp because it has two RCA outputs. It sounded terrible.
I think a preamp has the greatest affect on a system's sound. I have demoed a passive preamp, which does not use power. It simply chooses which input to feed to the amp and has a volume control. Theoretically, it is the proverbial straightwire that does not affect the sound. I didn't like it. The sound of my system became flat and the soundstage collapsed. When I went back to my ARC preamp, the soundstage inflated and instruments had bloom again. One might say that I preferred sound distortion. So be it. I much preferred my ARC to the passive preamp.
My point is that the preamp is an important part of your audio system, and you're going to have a preamp no matter what you do. I always think you should use your ears to evaluate a system component. Compare an integrated to separates in the same price range. See which one you like best. In other words, just because the preamp is built into an integrated doesn't mean you no longer have to think about how it affects the sound of your system.
