title_body: Does anyone have experience with this brewing method?
upvoted_answer: The biggest drawback is that you might add the grounds to too hot water. Especially avoid adding the coffee to water that is still boiling. Wikipedia has some references about the temperature and it states that boiling water will extract bitterness instead of aromatic oils. So just make sure to wait a moment after taking the water off boil.
  
  Second drawback is that since the grounds remain in the pot in contact with the water, you have to empty the pot entirely once the coffee is "done". Leaving the grounds in contact with the water for longer times will only add betterness to the coffee. Of course this is no problem if you only make one cup, but prepare to have a (pre-heated) container ready if making more cups.
  
  Related to the second drawback is that the extraction will continue in your cup because of the sediment, but in my opinion most people will not even notice it affecting the cup.
  
  Coffee oils make it to the news from time to time. Since this coffee is not paper filtered it contains more oils. Some like the taste, some do not. Some link coffee oils to cholesterol levels (I do not..), which might be a personal drawback to some.
  
  Offtopic: the method you describe is actually how my granny makes coffee, with a little twist (that I dislike). After adding the grounds, she heats the water to boil again and quickly removes it from the stove after first signs of boiling.
  
  Edit: Just wanted to mention that none of the drawbacks I listed is unique to this method.