An invoice is a piece of paper. A supplier under pressure can present the same one to two financiers in the same week, and neither knows until both come to collect.
Everything in a registry is visible to everyone who can query it. No supplier will publish their receivables book, because it names every customer and every volume.
Incomplete registries do not prevent double financing. Complete ones do not attract suppliers. That is the whole impasse.
A financier verifying an invoice tells the buyer their supplier needs cash. Suppliers avoid that call, so financiers verify less and price more.
Everyone is charged for the possibility of fraud they did not commit, which is what an unpriceable risk looks like in practice.
Design stage, nothing for sale. What helps is the real mechanics: what you verify before advancing, and what the gaps are worth.