If you generate a single initialization symbol that guards against multiple runs in the init section, this works just fine with dlopen.
This isn't even hard, but you need to be able to form a full dag of imports.
The only problem is that the linker slams together the .init, .ctors, or .init_array sections in some arbitrary order (usually the order that .o files are passed in on the command line, but there are no guarantees). If you topologically sorted the object and library list by import order, things would work out. But because the linker doesn't cooperate, a language that wants to avoid the initialization order fiasco needs to provide its own ordering. Or its own linker.
As far as Zig goes -- I have no clue what it does. Never touched it.
Also, as a side note -- initializers were initially designed so that there would be exactly one init function per binary or library, and then people wanted to split the initialization up, so the way the init section ends up getting constructed on most unixes is fascinatingly hacky: The linker links `crti.o`, your .o files, `crtn.o`. crti.o contains a function prologue; the init sections in your .o files contain a sequence of call functions, and crtn.o contains a function epilogue. Stitch them all together in order, and you get a single function that you can call.
This is deprecated, and now there's a table of function pointers (.init_array).
This is a very widely used capability and it is very definitely not trivial to just make an init function & define the import dag and have that work reliably. People will forget to call it & most of the time they won't have any clue what their dependency DAG even is. And that's assuming it can even form a DAG at all - cyclic dependencies are absolutely a thing, after all.
And I'm not sure how you can forget to import a library and still expect to use it, assuming your language has a module system.
C and C++ can't solve this problem, of course, due to textual inclusion.