As soon as this becomes a problem, then it might start bottom-up, citizens to government officials, rather than top to bottom, from president to government departments. Then governments will be forced to formalize identity solutions based on cryptography. See also this case in Germany [2].
One example like that, is bankruptcy laws in China. China didn't have any law regarding to bankruptcy till 2007. For a communist country, or rather not totally capitalist country like China, bankruptcy is not an important subject. When some people stop being profitable, they will keep working because they like to work and they contribute to the great nation of China. That doesn't make any sense of course, so their government was forced to implement some bankruptcy laws.
[1]https://www.wsj.com/articles/fraudsters-use-ai-to-mimic-ceos... [2]https://news.ycombinator.com/item?id=39866056
The thing about cryptography and government is that it's easy to imagine for a great technology to be adapted on the governmental level because of its greatness. But it is another thing to actually implement it. We live in a bubble, where almost anyone knows about cryptographic hashes and RSA, but for most of the people it is not the case.
Another thing is that political actors are tending to try to concentrate power in their own hands. No way they will delegate a decision making to any form of algorithm — being cryptographic or not.