I disagree that this method is not practical. If you had a look at the size of my garden you will see that it does work. An important step is to behead all dandelion flowers before they go to seed to minimise the volume of seeds. Of course there will always be influx of seeds from neighbours lawns who don't bother to keep them under control and the important thing is that you must never give up. It does take a lot of work initially but once under control, the removal of the odd dandelion isn't a major time user.
I have also used the mechanical removal method for capeweed which is a dreadful pest at my place and I hardly ever see any in my garden despite my neighbours having thousands of the pesky things. As soon as I see one it gets dug out and thrown into the chook yard where it lasts no time at all. High volumes get put into the compost heap or into the rubbish bin.
The secret of success is 'do not give up' and not a drop of herbicide is needed.
Allen
Australia