The ideal would be DNA-based authentication. You go to their store, they prick you and use rapid sequencing to verify that you are who you say you are.
How does the business know the DNA used to set up an account for Bob comes from him and not from attacker Bill? They would have to take his ID at his first visit so you’re still vulnerable to ID fraud.
We can argue back and forth but IMO the DNA idea has two problems: 1 It is too invasive as it requires customers to reveal their DNA to the business. 2 It is impractical. Firstly, the technology doesn’t exist. Secondly, it requires a physical visit to authenticate.
BBC News - India's living dead: 'They stared at me like I was a ghost' https://www.bbc.co.uk/news/stories-58259497
Biometrics are never perfect. Sometimes they can be forged (even something as simple as a printout of a human face looking in a camera), other times you take advantage of a tech vulnerability to feed the desired biometric data in directly without needing to produce anything physical at all.
https://en.wikipedia.org/wiki/John_Schneeberger
>John Schneeberger (born 1961) is a North Rhodesian-born former physician who drugged and raped one of his female patients and also his stepdaughter while a physician in Canada. For years, he evaded arrest by implanting a fake blood sample inside a plastic tube in his arm, which confounded DNA test results.
>During his 1999 trial, Schneeberger revealed the method he used to foil the DNA tests. He implanted a 15 cm Penrose drain filled with another man's blood and anticoagulants in his arm.[5] During tests, he tricked the laboratory technician into taking the blood sample from the place the tube was planted.
Wouldn't a finger print be easier?
Why would you need to go to the store plenty of dna sequencing happens over the mail for ancestry and alike. Partner with them and offer discounted dna results.
Ideally you do this once and keep a card and use it everywhere.
As to doing it by mail, that may be potentially doable, but one would need to think through how to prevent e.g. stolen saliva, MITM mail sample interceptions, etc.