That market is fragmented and disorganised and inefficient. But it’s deep, cross border and growing. Issuers write their own transfer policies which range from nope to fully permissive. The former aren’t interested in something like this because they aren’t focussed on shareholder liquidity. The latter don’t gain anything from forcing shareholders to only do business through Carta. (If they do want to do all that work, they can just do a tender. It is cheaper. And has no lock-in.)
This is a product in search of a problem.
Disclosure: I work in the private markets.