We have quite a good understanding that a system cannot be both sound a complete, regardless people went straight in to make a single model of the world.
Huh, what do you mean by this? There are many sound and complete systems – propositional logic, first-order logic, Presburger arithmetic, the list goes on. These are the basic properties you want from a logical or typing system. (Though, of course, you may compromise if you have other priorities.)
If you take multiple systems and make them work in concert, you just get a bigger system.
The conclusion may be wrong, but a "bigger system" can be larger than the sum of its constituents. So a system can have functions, give rise to complexity, neither of its subsystems feature. An example would be the thinking brain, which is made out of neurons/cells incapable of thought, which are made out of molecules incapable of reproduction, which are made from atoms incapable of catalyzing certain chemical reactions and so on.
This happens over and over with the relatively new popularization of a theory: the theory is proposed to be the solution to every missing thing in the same rough conceptual vector.
It takes a lot more than just pointing in the general direction of complexity to propose the creation of a complete system, something which with present systems of understanding appears to be impossible.