Why can primary cells not be recharged effectively?
Galvanic/electrolyic refers to how the cell is being run. If you have an electrochemical cell, and you connect a load to it, and it produces a spontaneous current, it's a galvanic cell. If instead you connect a voltage source, and the current from the voltage source induces a reaction, it's an electrolytic cell. There's no requirement that a galvanic cell be made with two beakers and a salt bridge, that's just a very common setup for introductory chemistry experiments using the Daniell cell.

The defining characteristic of a secondary battery is that the net "electrolytic" reaction is the reverse of the net "galvanic" reaction. So a secondary battery is a galvanic cell when it's discharging and an electrolytic cell when it's charging. In a primary battery, whatever reaction happens during charge doesn't return the battery to its initial state. A common reason for this is that the galvanic reaction produces insoluble products, so the concentration is really low by the electrode. Then when you reverse the current and run it as an electrolytic cell, something else reacts instead, like water electrolyzing.