Simmer, do not steep
A root or rhizome is dense woody tissue and hot water alone barely penetrates it. Ginger, turmeric, liquorice, dandelion, chicory and burdock all want simmering for ten minutes or more. Every tradition that drinks them boils them, and a cup of hot water poured over ginger slices is a much weaker drink than most people expect.
Roasted versus raw
Dandelion, chicory and burdock are roasted before use, and the roasting is what makes them drinkable — the raw roots are intensely bitter. Ginger and turmeric are used unroasted, dried or fresh, and dried is hotter and less bright than fresh rather than simply more concentrated.
The coffee-substitute tradition
Roasted dandelion and chicory both spread as coffee substitutes during nineteenth-century shortages and both world wars. New Orleans coffee is chicory-blended because of a Civil War shortage that ended 160 years ago. This whole sub-group exists because something else was unavailable.
Liquorice is the sweetener
Liquorice root is many times sweeter than sugar by weight and is used as much to sweeten a blend as to be drunk alone. If a herbal mixture tastes sweet and contains no sugar, liquorice is the usual reason.
Fat helps some of them
Turmeric is traditionally simmered in milk rather than water, and it is a noticeably better drink for it. Some botanical flavours are more soluble in fat than in water, and the traditions that drink them worked this out long before anyone explained why.