This means that each and every institution has to verify identities "from scratch" which they are not really capable of. Bootstrapping trustworthy verification of identity that is useful for commerce (e.g. where you can practically collect debts/credit and prevent creating fake identities so that you know who you're dealing with, can reach them for contract enforcement if needed, and can ban people you don't want to deal with) is really hard, so everyone is essentially delegating it to someone else - webstores to credit card issuers, all kinds of institutions to social security numbers, some to phone numbers, and everyone is doing that poorly and failing at making it secure since there is no solid foundation for any of it, resulting in the extremely costly identity theft problem (in USA it's like $50bn per year?) and in cases like this, where companies have to rely on "phone numbers" and ridiculous "security" questions like mother's maiden name - because they don't have anything better to use.
Privacy and anonymity are not the same; there are many domains where anonymity is reasonable and default, but also many domains where it is not; in those someone can respect privacy and at the same time refuse to deal with anonymous partners, and it's an entirely reasonable choice that they should be able to make not only in theory but in practice - having an effective, secure mechanism for a person to verify their identity to someone else.
Proper identities are a key basis for trust - without them you can do one-off immediate barters (perhaps many times), but prolonged relationships, various forms of credit and "credit-like-effects", accumulation of reputation are highly beneficial for society; and from the perspective of incentives it's worth noting that the harder it is to "get away with" betraying trust and start from zero, the less incentive there is to defect and more incentive to cooperate; there's a good reason why the game theory iterated Prisoner's dilemma (which relies on preserving identities) gets so much better average results for everyone than non-iterated or fully anonymized Prisoner's dilemma.