Here is a simple suggestion to make trait cycling more difficult to use reliably: For each trait played on a single character (that turn) the game deals 4 psychic damage to that character for each trait after the 3rd. The damage cannot be prevented. This would hamper trait cycling.
Not really... the chances of drawing 3 traits in a row is less that 20%, even with 12/36 traits in a deck. Drawing any more traits after that point is quite unlikely, and as such, your suggestion doesn't "reliably" do anything.