Do you think the advantages of paying tribute to the barbary pirates outweighed the disadvantage ?

Yes, i believe it did.
Compared to the maritime power of a kingdom, the power that held by the pirates at that time were relatively strong.
If the traders who want to pass want to ensure the safety of of their goods, they need to hire a group of mercenaries to accompany them.
The cost of mercenaries could even be higher compared to the tribute that required by the Pirates.