As long as nobody has forced you to join your computer to a domain and accept the installation of group-policy overrides, you're still fundamentally an administrator of that machine.

You might not ever feel the need to administrate it, because the OS vendor is often co-administering the machine (see: Windows or macOS when you use a local account rooted in their cloud SSO) but the OS vendor hasn't restricted you from doing your own administration in the way that a corporation or institution administering the domain your device belongs to would restrict you. You still have the ambient authority to administer your machine, whether you ever bother to elevate yourself or not.

You can still install your own X.509 roots of trust. Even on, say, iOS! (You must administer the iOS device using tools — e.g. https://github.com/ProfileCreator/ProfileCreator — that run outside of the device on a "real computer"; but that's just a fact of history, to do with how system administrators generally prefer to interact with computers, not a property of the target device's security. A config profile is just a file format; if someone ever wanted to make a profile editor that ran on iOS itself, they could.)

(And if we're talking about a machine that is corporate or institutionally controlled? Well, then it's the responsibility of the people who manage your device — your IT department — to decide whether a given cert should be given trust. Like it always was under X.509.)

> What is the technical challenge of setting up your own HTTP server that can be browsed with an off the shelf browser on your local computer?

The approach where you run a proxy that wraps untrusted connections into trusted ones is fully general, but yes, only really applicable to the most advanced users. But then, only the most advanced users really need and/or should want the full power of this approach. Only someone with a lot of experience in network security should consider themselves capable of vouchsafing a non-TLS HTTP connection as worth being trusted. You have to basically come up with a [continuously falsifiable!] "attestation heuristic" for the remote yourself — that it stays on the same IP, that its DNS records haven't changed owner, that the server is still sending the same Server response header, etc.

(In fact, if the point is just to look at old websites that were never updated to use TLS, it's probably better to let someone else solve this specific problem for you, through a full application-layer compatibility forward-proxy service like https://theoldnet.com/ .)

If your needs are slightly weaker — if you can assume that every remote is at least using self-signed TLS certs rather than not using TLS at all — then the problem is vastly simplified: you can directly trust any cert by putting that cert directly into your X.509 trust store (in effect making it a root-of-trust — though it doesn't have the X.509 property that enables other certs signed by the cert to be trusted transitively, so it's a leaf-node root-of-trust. A "stump of trust", if you will.) You don't need to run any local servers to do this. And, at least in some cases (e.g. macOS Safari) it's just a few clicks to get from "this cert is invalid" over to "add this cert as a root-of-trust" (i.e. https://i.imgur.com/IXpF4ld.png).

The only problem with this approach, is that there will be no continuity of identity if the X.509 cert of the remote gets to the end of its lifetime and must be renewed. You must act in the capacity of the CA, figuring out again, from scratch, whether the new remote cert should be trusted.

If your goal is to get together with a bunch of your buddies to escape the "X.509 CA cabal" by doing your own cert signing, you'd therefore be better off not using self-signed certs, but rather creating your own CA (probably an automated one using ACME!); importing that CA cert onto all your devices as a root-of-trust; and then having that CA sign certs for all your group members' sites. Then you'll get all the advantages of regular X.509, just in a sort of "overlay world" where your group's browsers can trust both regular sites and your private-world sites, while regular people who aren't part of your group will see a certificate error when visiting your group's sites (unless they also decide to import your CA as a root-of-trust.)

(TBH, this would be kind of a cool "member's only club" to join. In theory, with sufficiently-advanced ACME probes, you could also enforce whatever properties of each site you liked, at least at time of issuance. You could create an "overlay web" that acts like Gopher/Gemini or whatever else you like, just by doing this.)