While the UI is bad, I think the main reason client cents aren’t adopted is due to its cost and specifically recurring costs. For b2c stuff, users don’t want to purchase certificates just to authenticate. And they certainly don’t want to repurchase them every year or so. Imagine if a web site had an $80 annual authentication fee that didn’t even go to the site.
Way back, I wished there would be some sort of government issuance that would cover the costs and negotiate with standards people to allow perpetual client certs that never expire (good enough for bitcoin wallets).
Interestingly, the US government does do this for employees through the Homeland Security Presidential Directive [0] where all federal staff have a client certificate issued and stored in a physical card for use.
The UI is still bad, but you can use it to authenticate to federal websites.
[0] https://www.dhs.gov/homeland-security-presidential-directive...