Using a swift as a diaper bag
My wife and I have been using a swift with clear quarter packing cubes and the yarn stuff sack in various configurations as the diaper bag for our 10-month old boy for nearly 10 months. It has worked very well. You can attach the bags with long key straps to keep them from being left behind by accident.
The only complaint is that it gets heavy to carry with no shoulder strap after a while. Especially when packed for a long day. My wife liked it so much we had to buy a second one for her to use as a purse.
As for coolers or insulated pockets what we do for formula (breast feeding also, but having to supplement) is that we simply carry the bottles with measured amounts of water and the dry formula and a scoop separately. Then mix it up as needed and no need to refrigerate. Our son does not seem to care much about it being warm or room temp, or even kind of cold, most of the time. We of course heat it if possible, but when out and about, he doesn't seem to care.