Sizes of stdio FILE streams are still limited, because of ftell: the standard requires that file position (as measured from the beginning of the file) is representable as long or off_t.

You can advance an argument that even though each stream is limited, you can have an infinite number of streams, but this does not work, because stream name is a string, and there is only finite number of possible strings and the standard library does not contain chdir().

I think in the real world where a file can have a 64 bit size and long is 32 bits, ftell() can work or return an error depending on the size of the file. There isn’t really any other reasonable implementation in that situation.

So ftell() can exist but fail for unbounded seekable streams. The standard does not require ftell() to provide an answer in all situations.

Still won't work. The Standard explicitly specifies that FILE type includes all stream attributes, including position indicator:

    ISO/IEC 9899:TC3 7.19.1 
    FILE
    which is an object type capable of recording all the information needed to control a
    stream, including its file position indicator, a pointer to its associated buffer (if any), an
    error indicator that records whether a read/write error has occurred, and an end-of-file
    indicator that records whether the end of the file has been reached;

Hence no stream can be longer than 2^(sizeof(FILE)*CHAR_BIT) (6.2.6.1 guarantees that objects of any type cannot have "hidden" bits of state not accounted by sizeof()).