Quite simply, the Wal pickup has a unique, recognisable tone (at least to my ears). If you think about it, there are only a handful of bass guitars that qualify for this accolade: Rickenbacker, Fender, Alembic and maybe a couple of others. The Wal is there with them. The rest just go boom boom boom and you can only tell them apart by the player (well, that's how it [i]should[/i] be, I suppose).
Wal basses came to prominence at the same time as the bass guitar became a special feature in pop bands (when recordings sold in vast quantities) so everybody heard examples of the Wal sound a lot. The various famous players made a big impression and that has lasted over time.