The short answer is that computing power and resources advanced exponentially between the time that C was defined and the time that Java came along 25 years later.
The longer answer…
The maximum size of a compilation unit — the block of code that a compiler processes in a single chunk — is going to be limited by the amount of memory that the compiling computer has. In order to process the symbols that you type into machine code, the compiler needs to hold all the symbols in a lookup table and reference them as it comes across them in your code.
When C was created in 1972, computing resources were much more scarce and at a high premium — the memory required to store a complex program’s entire symbolic table at once simply wasn’t available in most systems. Fixed storage was also expensive, and extremely slow, so ideas like virtual memory or storing parts of the symbolic table on disk simply wouldn’t have allowed compilation in a reasonable timeframe.
The best solution to the problem was to chunk the code into smaller pieces by having a human sort out which portions of the symbol table would be needed in which compilation units ahead of time. Imposing a fairly small task on the programmer of declaring what he would use saved the tremendous effort of having the computer search the entire program for anything the programmer could use.
It also saved the compiler from having to make two passes on every source file: the first one to index all the symbols inside, and the second to parse the references and look them up. When you’re dealing with magnetic tape where seek times were measured in seconds and read throughput was measured in bytes per second (not kilobytes or megabytes), that was pretty meaningful.
C++, while created almost 17 years later, was defined as a superset of C, and therefore had to use the same mechanism.
By the time Java rolled around in 1995, average computers had enough memory that holding a symbolic table, even for a complex project, was no longer a substantial burden. And Java wasn’t designed to be backwards-compatible with C, so it had no need to adopt a legacy mechanism. C# was similarly unencumbered.
As a result, their designers chose to shift the burden of compartmentalizing symbolic declaration back off the programmer and put it on the computer again, since its cost in proportion to the total effort of compilation was minimal.