Let’s go through the advantages. And to be clear, this is about system where the pump is running directly off the solar array, without batteries. Control boxes are used much less often in system where batteries are involved.
A key feature of a pump control box is what is known as a linear current booster, or LCB. An LCB boosts the current from the solar array by lowering the voltage. This enables the pump to run in low light conditions, like in mornings, evening and cloudy days. The pump won’t be as productive as on a clear sunny day, but as the saying goes, 10% of something is better than 100% of nothing, and this case that proverbial 10% (or more) adds up over the years of service. And LCB will also create a clean break in the power from the array to the pump. Without an LCB an array can be producing some energy to the pump motor, but not enough to run the motor which creates arcing in the motor. This prematurely wears out the motor. With an LCB, it will not allow energy to the motor unless there is enough to make the motor actually run.
Control boxes usually have electric terminals for some type of switch, like a float switch or a pressure switch. Many switches are meant to only to send a message to the box to turn the pump on or off. They don’t have a thick enough gauge wire to actually carry the electrical load of the circuit between the solar array and the pump. This problem can be solved by getting a float switch with thick gauge wire, but they cost more and the length of the cable is limited because if the wire is carrying the electrical load then one has power loss to think about. Generally, it’s better to have a switch with a thin gauge wire that only sends a signal.
Control boxes vary in terms of the other features they offer, but often they include over voltage protection, fuses, manual on/off switches, indicator lights, and low water sensors for well applications. They can also add flexibility for array sizing. For example if one has a 24 volt solar panel and a 12 volt pump, the right control box can step down the voltage from 24 V to 12V.
All in all, if you want your system to run well, if you want to maximize the productivity, and if you want your pump to last, including a control box is money well spent. You won’t regret it.