Are there contemporary programming languages that do NOT have the ability to import functions or values or whatever from other files? Are there situations in which that would be a feature?
There's languages designed with Capabilities in mind. Like, whatever starts the program gets to decide what functionality is exposed to the running program. It's great for situations where you might run untrusted code and want to, as an example, not allow network access, or filesystem access.
More generally there's also sandboxing techniques that runtimes provide. Webassembly for instance is designed for programs to run in their own memory space with a restricted set of functions and, again, Capabilities. This might be nice if you ever work on a cloud application that allows users to upload their own programs and you want to impose limits on those programs. Think AWS Lambda, except the programs running wouldn't necessarily even have access to the filesystem or be able to make web requests unless the user configures that.
It might be a good design space for even more esoteric areas, like device drivers. Like, why worry if your GPU drivers are also collecting telemetry on your computer if you can just turn off that capability?
There's older applications of sandboxing that are a bit further from what you're asking as well; like, iframes on a webpage; allowing code served from different servers you don't necessarily control to run without needing to worry about them reading access tokens from local storage.
I guess a more modern example you might run into is something like Rust's no_std environment; which strips out the standard library of the language that doesn't work on every device the language is designed to target (namely microcontrollers that don't even have an operating system on them). Or like, maybe you're writing your own operating system.
Another example comes to mind of a company, General Magic, that designed a programming language with a similar Capabilities system meant to restrict access to functions and code on their devices with the idea of copyright enforcement in mind as a primary use case. There's a documentary about the device if you're interested: https://www.generalmagicthemovie.com
Deno is an example of a language runtime (based on Javascript+Typescript) that's been built with capabilities in mind. By default, programs aren't allowed to touch the filesystem or network (except to allow static imports to run; fallible dynamic import calls that could be used to determine something about the filesystem or network are restricted like other IO). Programs can start up worker threads that have further permission restrictions than the main program.