PE would know better than me for sure, but I would assume there must be some additional compounds in Kodak's single packets that not only allow all the main ingredients to be stored together, but also allow them to go into solution together.
Regarding storage, note that Ilford's equivalent MQ film and paper developers are packaged in two packets.
Regarding mixing, for example, my understanding is that Metol will not readily dissolve in Sodium Sulfite solutions. This is why whenever both Metol and Sodium Sulfite are called for, the standard mixing practice is to dissolve only a pinch of Sulfite (to scavenge some Oxygen) before dissolving the Metol. The rest of the sulfite must go in at some point after the Metol is dissolved.