Because the OS data doesn't provide addresses, just locations of the postcodes in coordinate terms, so you can't provide the typical website address lookup.
I can't find any good information post-privatisation, but at least before 2013 the postcodes themselves were copyrighted by Royal Mail (likely Crown Copyright as with government data). There were attempts to enforce this in 2009[0]. I suspect the copyright is now owned by Royal Mail Group Ltd.
That aside, a practical issue is that Royal Mail still retains the rights to _allocate_ new postcodes for any new properties. Yet another failure of this particular privatisation.
> Oh, and it wouldn’t even be legally allowed to include, er, postcodes, as they are specifically owned by Royal Mail