I contacted their customer service. They explained that they require to re-KYC every account that has been inactive for 60 days. It is a rather short period, but more or less understandable for an enterprise-oriented provider. However, they declined to answer why they have choosen such an invasive KYC method, citing unspecified "security reasons".
Following my own research, I suppose it might be due to a certain FCC case[1], in which a scam caller used Telnyx services. It would explain why the KYC procedure is required in order to place calls, but does not explain it as a condition of logging in to the service.
I'd rather not upload my biometric data to who-knows-where, both because I find the whole recent AI-powered surveillance boom distasteful, and also because that specific company has suffered a major data breach[2].
1. https://www.bleepingcomputer.com/news/security/robocallers-posing-as-fcc-fraud-prevention-team-call-fcc-staff/ 2. https://cybernews.com/security/popular-apps-left-biometric-data-ids-of-millions-of-users-in-danger/