Nuxt should export the static site with asyncData removed. It isn't needed for static export (payload.js is used instead) => unnecessary data for the user to download.
Nuxt keeps asyncData.

It is still necessary for the following situations:
Hello @manniL
thank you for your reply! I've some questions.
In case the payload can't be fetched
When can't the payload be fetched? If the user lacks of network access? The API would be unavailable, too.
When using SPA fallback (no payload in this case)
Isn't the full static export a static site which hydrates to a SPA without API requests? => we don't need asyncData.
When using preview mode
What do you mean with "preview mode"? Running Nuxt in dev?
When can't the payload be fetched? If the user lacks of network access? The API would be unavailable, too.
The most common situation I can think of is when using the SPA fallback (as there won't be a payload). But there might be other scenarios where this comes in handy instead of letting the site break.
When using SPA fallback (no payload in this case)
Isn't the full static export a static site which hydrates to a SPA without API requests? => we don't need asyncData.
Yes, this is correct so far. But you can exclude routes from being generated (e.g. everything behind authentication). Those have no payload but can still be accessed "normally" and will load as "SPA" (no generated HTML)
When using preview mode
What do you mean with "preview mode"? Running Nuxt in dev?
See https://github.com/nuxt/nuxt.js/pull/6159#issuecomment-631608962
@manniL
Thank you very much for answering my questions! It's clear now 馃槈