Why would a small protein have an nls, when it naturally diffuses across the nuclear pore complex without one?

An NLS or nuclear localization signal refers to a sequence of amino acid, which tags a protein for import into the nucleus of the cell by nuclear transport. Generally, this signal comprises one or more brief sequences of positively charged arginines or lysines visible on the surface of the protein.

The small protein would exhibit an NLS, as it is used to actively import almost all the protein within the nucleus, leaving behind very less protein in the cytoplasm. The process of diffusion would not mediate all the protein within the nucleus.