It is my understand that, originally, the scallop shell was presented by authorities at Santiago as a sign that the holder completed their pilgrimage. It was more durable and wearable than a parchment Compostela.
Indeed, some European pilgrims were buried wearing their conchas. Back in the day, having completed and survived the Camino, and returned home to tell about it was a HUGE accomplishment. When living in Belgium for a few years, I even saw gravestones engraved with conchas. One presumes they wanted all to know that 'here lies a pilgrim." Others may know more about this.
However, and again, way back when, unscrupulous vendors along the Camino began to offer these shells to anyone who paid their asking price. Over time, the scallop shell then became a useful badge to identify one as a pilgrim enroute to Santiago, instead of one who had completed a Camino. Over the years, the latter context has become the default context. You wear a shell, people recognize you as a pilgrim on The Way.
Along the way, the shell might also have been helpful as a drinking cup, spoon type device for eating from a communal pot, a musical instrument (when two are rubbed together back-to-back), or a tool for use where some sort of scraping action was needed. It served as sort of a multi-tool of the time.
For reference, and unless something has changed, the shells offered at St. Jean Pied de Port are of the plain, unstenciled variety. I was told they are obtained from local restaurants that offer Coquille St. Jacques on their menu. Now, you know where the name of this popular French entré comes from.
These shells do not have the red, painted-on with a stencil, Cross of Santiago. At, the Pilgrim Office, this is one way I use to identify someone who has walked from StJPdP. Most all other shells obtained at any other place, including the Pilgrim Office, are obtained from commercial vendors who pre-apply the Cross of Santiago, using a stencil. This is only suggestive, not categorical. But, it gives me an opening for a polite chat about their Camino while they are waiting on line.
I hope this helps.