I would like a way to redirect someone to their own profile page, instead of a pre-defined page name like "welcome".

For this to work for all users, it needs to be a solution that can redirect based on either a user's ID number (supporting the Per-site Profiles feature) or a user's UNIX name (which many free sites already use for custom profile pages).

Current workaround

The current workaround at the moment is to send all new members to a page such as _default:welcome, and include a ListUsers module on that page to construct a link to their profile:

[[module ListUsers users="."]]
    [/profile:%%number%% Visit your profile page!]
[[/module]]

Yes, the workaround actually works. But sending people directly to the page instead of telling them to manually click the link would mean a better user experience.

Suggested solution #1

The first solution I came up with for this would be to accept variables in the "Welcome page for new members" field (Site manager > General settings), not just a plain page name as it does at the moment.

e.g.
profile:%%user_id%%
member:%%user_unix%%

Suggested solution #2

Another possible solution would be to accept variables in the Redirect module. We could set the welcome page to be something like _default:welcome, and then put this code on the page:

[[module Redirect destination="profile:%%number%%"]]