Does anyone have experience with this brewing method? The question here is about the following primitive method for making coffee. Having used this method for many years now I think it gives consistently good coffee, comparable to that from a good espresso machine but without the need for machinery or paper filters.

Recipe: Bring one cup's worth of water to a boil in a small pot. Add about a scoop and a half of ground decent-quality beans to the pot. Swirl gently until chalky bubbles appear. Filter through a tea strainer into a cup. Let stand briefly. 

No need to grind the beans to a powder. The tea-strainer gets most of the grounds and the amount of sediment in the cup is about the same as in cafe espresso. The only electric component is a coffee grinder. Using pre-ground beans requires more coffee per cup, as some flavor will be missing.

In general this method produces coffee that is slightly weaker than espresso. While I might add a bit of sugar to espresso to counter bitterness if the beans are old or mediocre, the strainer method above gives coffee that is very drinkable without sugar. 

It sometimes surprises me that this simple method isn't more widely used. Has anyone else tried it? Are there any drawbacks to this method? It isn't worth much commercially because it only makes decent coffee one cup at a time.  

This method is adapted from one I saw used by fisherman in Brazil, except he used a sock instead of a tea strainer. Comments welcome.
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.