mock-http-server | Simple HTTP server written in PHP to make HTTP | Mock library

Is this not how people do acceptance testing in the Node universe? Does everyone just use a fixed set of mock data for their entire test suite?

No. You don't have to make actual HTTP requests to test your apps.

All good test frameworks lets you fake HTTP by running the routes and handlers without making network requests. Also you can mock the functions that are making the actual HTTP requests to external APIs, which should be abstracted away in the first place, so no actual HTTP requests need to take place here as well.

And if that's not enough you can always write a trivially simple server using Express, Hapi, Restify, Loopback or some other frameworks, or plain http, or even net module (depending on how much control do you need - for example you should always test invalid responses that don't use HTTP protocol correctly, or broken connections, incomplete connections, slow connections etc. and for that you may need to use lower lever APIs in Node) to provide the mock data yourself.

By the way, you also always need to test responses with invalid JSON because people often wrongly assume that the JSON they get is always valid which it is not. See this answer to see why it is particularly important:

• Calling a JSON API with Node.js

Particularly since it seems like it wouldn't be that hard to write a good one based on express server that has all the necessary features... does it exist?

Not everything that "wouldn't be that hard to write" necessarily has to exist. You may need to write it. Hey, you even have a road map ready:

Necessary Features:

1. Server can be configured and launched from javascript
2. Responses(including headers) can be configured on the fly
3. Responses can also be reset easily on the fly, without shutting down the server.

Now all you need is choose a name, create a repo on GitHub, create a project on npm and start coding.

You now, even "it wouldn't be that hard to write" it doesn't mean that it will write itself. Welcome to the open source world where instead of complaining that something doesn't exist people just write it.