Why do functions need to be declared before they are used?

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How do you propose to resolve undeclared identifiers that are defined in a different translation unit?

C++ has no module concept, but has separate translation as an inheritance from C. A C++ compiler will compile each translation unit by itself, not knowing anything about other translation units at all. (Except that export broke this, which is probably why it, sadly, never took off.)
Header files, which is where you usually put declarations of identifiers which are defined in other translation units, actually are just a very clumsy way of slipping the same declarations into different translation units. They will not make the compiler aware of there being other translation units with identifiers being defined in them.

Edit re your additional examples:
With all the textual inclusion instead of a proper module concept, compilation already takes agonizingly long for C++, so requiring another compilation pass (where compilation already is split into several passes, not all of which can be optimized and merged, IIRC) would worsen an already bad problem. And changing this would probably alter overload resolution in some scenarios and thus break existing code.

Note that C++ does require an additional pass for parsing class definitions, since member functions defined inline in the class definition are parsed as if they were defined right behind the class definition. However, this was decided when C with Classes was thought up, so there was no existing code base to break.

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