Division of labor, for one thing...
...each power supply can "concentrate" on it's specific task...flexibility is another. You can change/upgrade components easier...insert processors without using tape loops...if your pre- goes south you can plug your high-level sources directly into your power amp, as long as they have a volume control, that is. Perhaps you like features on a pre-amp that aren't available on an integrated, might be another. Maybe mono-block amps located close to your loudspeakers are what drives you...separate components are the only way to fly in that case.
I have a "vintage" integrated I use as a pre-amp/control center...two tape mon loops and other switching functions...wouldn't trade it for anything...started out using it as an integrated...upgraded with a higher powered power amp and used the internal stereo amp and an ambience enhancement unit to drive my rears...that worked out best for my purposes...
There are strong arguments for recievers and other combinations, it really depends on your long term goals.
Nowadays, with multi-channel and processing, it's gonna' get a little hairy wiring things up if you go separates...but you do retain that flexibility IMO.
jimHJJ(...just my take on things...)