Trust On First Use is the normal thing for these situations.

TOFU equates to "might as well never ask" for most users. Just like Windows UAC prompts.

You're right most of the time. But there are two webs. And it's only in the later (far more common) case that things like that matter.

There is the web as it always has been on http/1.1 that is a hyperlinked set of html documents hosted on a mishmash of random commercial and personal servers. Then there is modern http/2 http/3 CA TLS only web hosted as a service on some other website or cloud; mostly to do serious business and make money. The modern web's CA TLS-only ID scheme is required due to the complexity and risk of automatic javascript execution in browsers.

I wish we could have browsers that could support both use cases. But we can't because there's too much money and private information bouncing around now. Can't be whimsical, can't 'vibe code' the web ID system (ie, self signed not feasible in HTTP/3). It's all gotta be super serious. For everyone. And that means bringing in a lot of (well hidden by acme2 clients) complexity and overhead and centralization (everyone uses benevolent US based Lets Encrypt). This progressive lowering of the cert lifetimes is making the HTTP-only web even more fragile and hard to create lasting sites on. And that's sad.

TOFU works for the old web just great. It's completely incompatible with the modern web because major browsers will only ever compile their HTTP/* libs with flags that prevent TOFU and self-signed. You could host a http/1.1 self-signed and TOFU but everyone (except geeks) would be scared away or incapable of loading it.

So, TOFU works if you just want to do something like "gemini" protocol but instead of a new protocol just stick to original http and have a demographic of retro-enthusiasts and poor people. It's just about as accessible as gemni for most people (ie, not very) except for two differences. 1. Bots still love http/1.1 and don't care if it's plain text. 2. There's still a giant web of http/1.1 websites out there.

Not to mention the usage of web browsers for configuring non-internet devices! I mean such as managing a router from the LAN side built-in webserver, how many warnings you have to click through in Firefox nowadays. Hooking an iPhone to an IoT device, the iPhone hates that there's no "internet" and constantly tries to drop the WiFi.