There is nothing wrong as such with the integrated bags/seats and I am not trying to knock anyone who uses them. Plus as you rightly say Trotter if the bag bit clips on or off then you have the best of both worlds anyway
Just in my opinion having a separate bag and seat is an advantage (for me) because I can have the bag sat next to me rather than below me which makes access to it easier as I dont need to twist round or get up to get into it and also means I can position the seat in say the mud or water but the bag out of the mud.
It also gives you more options in terms of the type of chair you want. You can go for a mega lite stool or if you are prepared to add a bit more weight a proper fishing chair...backrest, adjustable legs etc etc.
Also it means I have more flexibility in how I position anything I carry. For example Sometimes I hang things off my chair like a bucket of bait or I stuff a rod rest into the chair with the bag on my back.
Basically i think it gives you more options and is a bit more flexible.
One other tip ...on the advice of this forum I got myself a JRC Xlite stealth chair and I have to say its really the chair I have been searching for, for a very long time. Ultra lite, comfortable, fully adjustable ...it really is great. Costs a bit but from what I have seen will last for years as well. I am as aware of carrying un-needed weight as anyone believe me having suffered from allot of back problems but that bit of kit really is good.
Of course many people do away with a chair altogether. I sometimes do myself for very short sessions.