It's all a matter of relative solubility:
Potassium sulfate: 12g/100mL water at RT, 24.1g/100mL at 100°C
Potassium hydroxide: 107 (at 15°C), 178 @ 100°C
Sodium sulfate: 11 @ 0°, 92.7 @ 30° (probably way higher at boiling)
Sodium hydroxide: 42 @ 0°, 347 @ 100°
So, looking at that, you're going to have a hard time getting the reaction to go. Since potassium sulfate is the least soluble component, you're going to be hard pressed to force equilibrium to the right. At room temp, it's the least soluble component, and at higher temps, it's still the least soluble component.
Don't know why anyone would want to make KOH this way since you can just buy it at the store anyway.