A few notes:

• It should be noted in the interface that this reason will be made public on their user page.

Like:
Short message describing what you would like to do on Wikipedia: [ ....... ] (optional) (will be made public on your user page).

• The "registration succesful" page could perhaps include a link like " Edit my user page".
• When creating an account the userpage would be created with msg "userpagefromaccountpurpose" containing something like "== What I would like to do on Wikipedia == \n $1". Which wikis could modify as they like.

FT2.wiki wrote:

Agreeing with both the above.

FT2.wiki wrote:

(Although make sure that anti-vandal tools such as abusefilter and RC feeds see the proposed post, otherwise it becomes a vector for unchecked posting.)

As commented by phoebe ayers at foundation-l:

See also http://outreach.wikimedia.org/wiki/Account_Creation_Improvement_Project

This has already been done for account creation by existing account, but it's not what meant here: replacing "purpose" with "motivation" because otherwise it looks like our standard summary/reason/justification fields.

This seems a bit like Translate extension's Special:FirstSteps: https://translatewiki.net/w/i.php?title=Special:FirstSteps
Surely not a site request; I doubt it's suitable for core either, but for now I'm moving it to MediaWiki nevertheless.

https://www.mediawiki.org/wiki/Developers/Maintainers has no maintainer for Special pages, where User login lives. I guess this task is "Needs Volunteer" in a best case scenario.

Most of core is unmaintained. That's no indication of priority.