The shorter and cleaner the signal path, the cleaner and clearer the sound. If an integrated amp has the same quality preamp circuitry as separates, eliminating the cable between a preamp and amp will improve the sound. Same with a phono stage. The problem is, this is not usually the case. But sometimes it is. My system sounded better with a separate phono stage, despite the extra cable, because the phono stage was of much higher quality than that in the integrated amp, which is very good.
Same thing with features. Adding more circuitry for features like bass and treble controls and balance adds to the circuit and creates noise. I suspect adding a DAC or streamer creates noice to the amp/preamp circuitry as well.
Having a tonearm cable not directly into the cartridge adds another point of distortion. Separate headshells make changing cartridges convenient, but one cannot possibly argue that another point of signal transfer doesn't add distortion. Everything is a tradeoff.
My integrated amp has a remote for volume and mute only. I made the tradeoff when I was too lazy to get off the chair to adjust the volume. Since I only listen to vinyl, no need to be able to switch sources, which thankfully the amp's remote can't perform. And sure as heck don't turn the amp's power off with a remote.