Why does electrolysis take so much time?
It depends: The rate of electrolysis is limited either by the electric source or by the ion concentration. I am inexperienced with electrolysis but I imagine that quality may increase as the the process slows, much like crystals grow with more imperfections when the rate of crystallization is fast. 

There is no such thing as an electrolyte solution composed of positive ions and electrons. 


  "Activity coefficients of single ions cannot be measured
  experimentally because an electrolyte solution must contain both
  positively charged ions and negatively charged ions." -Debye–Hückel
  theory


Electroplating systems tend to use an electrode source that replenishes the solvent ions plated onto the target electrode.