Today, everyone can suggest post edits. Even unregistered users. But, for some reason, tag synonyms suggestion is very strict, although it's much easier to review - it's only a couple of words.
I think that a good taxonomic system will improve the odds of finding an answer and avoid duplicate questions.
I'm suggesting to lower this limit dramatically. IMO, a 500 rep user is well acquainted with the system and understand the meaning of tag synonyms to suggest some of it's own.
Current tag synonyms suggestion policy:
Users with more than 2500 reputation and a total answer score of 5 or more on the tag, can suggest tag synonyms. Users with a total answer score of 5 or more, can vote for tag synonyms. Suggestions will be automatically approved when they reach a score of 4, and automatically deleted when they reach a score of -2.