Note that amongst my qualifiers was unity of client and builder-architect.
You'll find plenty of examples of people on DIY or lone-inventor projects saying "we tried X, it didn't work, so we did Y instead. That's the unity-actor case of your hypothetical.
Dividing executive-agent roles is a complexity dimension.
Dividing executive (decision), design, expert (engineering), sourcing, external approval, interface, and labour/crafstmaan roles are multiple additional complexitty dimensions. And this doesn't even include the technical dimensions of the project and its infrastructure interfaces / interconnects.
Complexity is interaction between components and entities.