The largest advantage of making connections was the concept of specialization.
Tycondrius was very good at several things. He was not the best at any of them, but he was acceptably talented at waging war, training, and... gathering a half-dozen or so relatively useless fools and forcing them into doing something... useful.
For balancing books, Tycon could have attempted to fix it all himself... but a far more efficient and effective solution was to call in a specialist. Through the Courier's Guild, he sent out a few letters, including a discrete letter to Sorina Capulet, the Bronze-Rank Calculator that was Sol Invictus' Chief Financial Officer. Barring any fantastical incidents, she would make her way to the Holy Country's city of Silva as soon as possible.
Invictus note: Tycon still runs faster than Sorina, gauging by the (somewhat confusing) letters he receives from Korr. If it was not obvious, Tycon’s running speed is slower than that of Corporal Horse and Private Jeremy.