I built Checkr's background check ETA in Ruby/React, and had to get background check certified to work there. Part of onboarding was going down to the courthouse to show us how it was done before APIs. While it's true some records are still offline in some courthouses, almost all of it is online, some is even sold to 3rd parties in some states like mugshot websites, background check sites, etc. While others are on-prem servers the state/county runs. But they definitely use databases and computers lol.
I think you're missing the point - you act like I'm suggesting AI replace the entire legal system when I'm talking about a tool people would use instead of older tech like a SQL database and UI.
For courthouses that run their SQL on-prem for security reasons, could do the same with models - they don't even need access to the internet. So if you wanted to be inaccessible to the public you could (though some states/counties require they make it public).
Nothing will satisify the neo-luddite take, just watch from the sidelines I guess!