In order for chemical analysis of glass to really work in terms of sourcing where the glass is coming from, we have to assume that each glass-making workshop has its own unique chemical signature. Otherwise, we can’t use chemistry to source the glass.
This could be a reasonable enough assumption if we concentrate specifically on trace elements. Proportions of the main elements in glass may vary enough between regions, but there are only so many glass recipes, and having the major elements be that different (though potentially possible) seems overly optimistic to me.
But that’s not the only assumption we gave to make if we want to source glass through chemical analysis. We also have to assume that each batch a site makes of at least a specific colour is consistent in its chemistry. If one batch differs significantly from another, then chemical sourcing becomes much harder. In the end, we need as little chemical variation within a manufacture site as possible and as much chemical variation between manufacture sites as possible.
And the final large assumption we have to make is that the chemical composition we see in finished products (like beads) comes specifically from the original act of making glass, rather than recycling or some other chemically altering process. With glass, particularly glass in Europe, this is a huge assumption to make. There is rampant evidence throughout the continent for glass recycling, which often changes the chemical signature.
This doesn’t necessarily mean that chemical analysis isn’t useful – it certainly is, and the sooner we can find an inexpensive, non-destructive method for analysing glass that also measures all the elements we need, the happier I will be. But we also need to be extremely cautious in how much credence we give to chemical analysis when it comes to sourcing glass.