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none of what you said is wrong but it’s not peculiar to private shares. Public shares are directly analogousMost publicly-traded shares are held in street name. (Most but not all of those are with Cede & Co, but again, that's a technicality.) There is no common analog for street-name holding in the private markets. (Idiots keep trying to create it.)
> most founder shares are directly listed with a transfer agent (in the west probably at Computershare)
Yes, if you're a founder, "holding" shares on Carta is similar to "holding" shares that are publicly traded. I'm assuming someone asking this question isn't the founder.
> philosophically Fidelity failing _doesnt_ impact your legal claims precisely because Cede & DTC exist
There is no philosophy. Legally, if Fidelity fails, you have a claim on Fidelity and the SIPC. They have claims on Cede & Co. But in a very real sense, you "hold" your shares there.
Practically, Fidelity is unlikely to fail for a host of reasons. Maybe a less incendiary example is this: if Fidelity wants to freeze your shares, they can freeze your shares. They control them. If LTSE...E wants to freeze your shares, the company can overrule them. LTSEE isn't a "golden source." Put another way, Carta != EquityZen. (Though I think they also launched an SPV product?)