Entering search from a Profile page (mine or another member’s) the search facility automatically prefers posts by that member. Likewise from within a category.
Both those things are useful as an option, but frequently they’re not what I want, and it’s irritating to have to return to the home page to get an “unbiased” search.
Is there any way for the user to take control of search preferences, rather than Discourse?
Not at this time, no. You can always use Google with the site: operator for power user stuff. Visit any 404 page on the site to get a Google search box shortcut.
True, but will a Search give posts that are hidden or deleted?
I’m guessing that @TechnoBear is more interested in Moderation stuff than “interested in”. results.
I’m not thinking necessarily about moderating or about “power user stuff”.
I may be viewing one forum when something I read triggers a memory of another post I want to look at again. If I happen to know that post is in the same forum, then having the search results favour that forum is OK. If I happen to know the post is not in that forum, then to stop the results showing a bias, I need to leave that forum (and the thread I’m reading) to get an unweighted search.
Disruptive and not very convenient.
Eventually we plan to have a full page search with more power user options. Right now we are favoring simplicity and what works for average users in search.
We created a first version of full page search as a discourse plugin.
It has some power user stuff like sorting and category faceting. Room for improvemend interface wise, though. Not sure when we’ll have time for polishing.
The main request was satisfied here: the search within user, category or topic is an explicit checkbox underneath the search (and it will be 
if you begin from a user page, category page, or topic page respectively, but can be unchecked).
So it should be more clear now what’s going on and you can control it.