Which KYC provider would that be? He would have to be approved by everyone, and the most reliable possible.
As I wrote, one example is SumSub. Others are Trulioo, Shufti, Neokred and ID.me.
This also requires the participation of other governments, where they will agree to expose the data of their citizens at anyone's request. For example, some scam exchanges can be made to collect data using this method.
Yes, and that's one of the parts of that method I don't like. For this reason this is of course not available in all countries (my country for example is listed as one where it's offered - I can't imagine how a government can offer such sensible data securely that
leaked personal data of 25,000 citizens stored by their migration office to a hack only few years ago so it makes me a bit afraid.

But KYC systems where the data can stay on the device the liveness check is done, or are at least not stored online, look a bit more promising.
I asked Gemini more about KYC methods which do not store data online, and that's what I got:
Some advanced liveness detection systems are designed to process biometric data directly on the user's device or to generate a one-time verification template that is later discarded, to minimize the long-term storage of raw biometric information. However, this is not a universal practice.
And when I asked for examples it listed the following companies:
Mitek Systems: Offers solutions like Mitek's MiPass and IDLive technologies, which are designed to improve secure user authentication with face and voice liveness detection. Their approach emphasizes security and compliance through methods that generate secure biometric templates, which are mathematical representations of biometric traits that cannot be reverse-engineered back into the original image or video.
Trueface (acquired by Sensity): Provides edge-based, passive on-premise face liveness detection solutions. Their technology is specifically designed so that liveness checks are performed entirely on the device, often without an internet connection, and no data leaves the device.
Innovatrics: Their facial recognition technology includes options for advanced "on-edge" video processing. This allows for the capture and processing of data on the device itself, making it suitable for applications where connectivity is limited and privacy is a priority, with liveness detection capabilities built into their SDKs.
MiniAiLive: Offers an Android SDK for face recognition and 3D passive face liveness detection which is fully on-premise, meaning all processing happens on a local server or device, and no data leaves that environment for cloud storage.
iProov: Focuses on secure, user-friendly passive liveness detection. While most systems communicate with a cloud service to verify the data, iProov's approach to "Genuine Presence Assurance" involves advanced methods to confirm the user is a real person at that moment, often using patented light-based technology to secure the process, emphasizing that a fleeting, secure scan is what leaves the device, rather than stored raw video data.
I don't fully understand the last solution but the others look actually quite interesting. Technically, these methods should not be problematic at all, and it should be difficult that a criminal "hacks" it (if there are no bugs) if all processes are encrypted and digitally signed.
An open source solution for this kind of KYC processing would be ideal in my opinion, where the user can confirm that indeed no raw biometric data leaves the device, only consulting the code.

PS: I've added the "on-device processing" option to the OP.