Smartcard + faceid?
You're missing the point.
The solution is for the tech people to stop thinking they're the center of the universe, and drop requirements that make no sense for their users.
In the case of the death certificate, that means dropping the extra authentication requirements for that computer application*, or just having the doctor print out the certificate and sign it, like it was always done.
* Software engineers suffer from a certain kind of brain rot where they assume the computer system itself is the last and only line of defense (so enforce onerous authentication requirements). In some cases that might be the right call, but in others is makes more sense to loosen the requirements and rely on other systems (e.g. auditing and after-the-fact investigation).
Doctors are also known for superiority complexes. Took forever just to get them to wash their hands to prevent contagion spread, historically speaking. They are not special snowflakes nor gods, but yet another stakeholder in a system. Their feedback should be used to improve systems as I mention above, to assist them but not block them. Change is inevitable.
https://www.cmu.edu/dietrich/sds/docs/loewenstein/physicianN...
https://www.nationalgeographic.com/history/article/handwashi...
(not a software engineer, head of security, including anti fraud measures)
There's probably not a whole lot of massively society-impacting fraud in the death certificate system if a whole hospital can run off of technically fraudulent records when one guy is signing them all.
You could cut down on that by relaxing the technological attempts to "improve" it all and just let the legal system and humans address any actual abuse.
It should be noted that absolutely none of those goals were achieved by the above-mentioned poorly implemented biometric requirement. The only thing that achieved was inconvenience that needed to be worked around to get the real job done.