I actually like the site search engine and find it works better than external search engines for about 90% of my searches, is far more flexible in terms of narrowing by user, section and finding the term I want. Of course I have no cooldown thanks to the fancy colours in my title so I can recursively search instantly if I typo or I cook up a better search. 90% of the time I am searching for something I remember and just need to link though, or expanding a given topic and checking something else (I find a new magic stamp for something I am hacking and I search that to see if someone else found something before me).
With that in mind I have to ask what issues the OP, and others, have with the search. Does it fail to return results that should have been there (a popular thing with search engines and large databases these days but not necessarily something I have seen here*), are the word length/commonality limits too harsh (possible, especially given how people like to abbreviate -- most 3 and 4 letter abbreviations are not going to happen), some of the examples given would probably be better served by making sure sticky articles and the wiki are up to date
You ponder whether having things repeated may add to the noise and make searching in general and refining by date harder. This is certainly possible. Google tried to solve this initially with their link rating algorithm (more people link to you, higher up in the rankings), here would probably be something like views (urgh), likes (double urgh) and replies (more urgh).
Equally your example used the rather human phrasing of "how do I". I have never gone in for that -- the ask jeeves search engine famously showcased such a thing and I thought it was a stupid idea then as it felt redundant not to use key word searches. It is slightly better if you are looking for a basic article with a title on how to do something there and then, but not by much.
*Ignoring that Google is a famous user of sub optimal searching then I do have to say Google's auto correct spelling, did you mean, general synonyms vs strict search and lack of fussiness with some types of grammar ('s might trip up the basic forum search engine where google would not care, that is a fairly serious search addition though).
I could go on but I have some stuff that needs doing so I will leave it there for now. There is certainly scope to improve things but at what cost and might it also be an operator failure?