Hydraulic separation in hydronic systems is generally more important with high flow resistance heat sources such as condensing boilers. If you don't hydraulically separate the heat source from the rest of the system, then you will have unnecessarily large pressure drops through your boiler. In order to have "complete" hydraulic separation, it is not necessary to decouple both fluid streams, however, as your question seems to indicate. By using either a hydraulic separator or closely spaced tees (perform the same basic task as a hydraulic separator without the expensive specialty equipment price tag), the two different circuits (one for your boiler loop and one for your primary loop) can each perform their functions separately.
The use case for a heat exchanger decoupling the fluid stream completely would be better usually only when one fluid stream cannot be mixed with another due to additives or contaminants, but the heat transfer will not be as efficient.
Caleffi (an Italian hydronics brand) has some excellent resources and explanations in their Idronics magazines that they release every so often.1 Of particular interest might be #19: Proven Hydronics Systems.