It's clear it wasn't Shiroe's intention to build a tyranny, so it goes without saying they don't consider abuse of power the first solution to problems, despite having the resources to solve everything external with it. His intention, that the other members of the round table seem to agree on, is to build normal relationships with the surrounding people of the land. If they relied too much on power, I don't think they would easily win the trust of all the adventurers either. I don't believe the players at large still consider the round table a real government with authority the same way they tought of the governmental system of Japan back in RL. The majority probably views the round table as a gathering of guild leaders who handle foreign affairs and laid down some internal codes of conduct that majority could accept and thus live more easily in Akiba. But that's still no different from joining a random web forum and honouring the posting rules, more or less. Maybe the round table members are more like the moderators of Akiba in their minds.

Besides, this whole incident, like I said earlier, is so far largely between people of the land with Akiba and the adventurers being used as tools in the middle of it. That might naturally change, and the preview suggested as much, but there's not really awfully much for Shiroe to be concerned about right now, certainly not to the point of resorting to assassinations. He could even view this as a fire drill. Who knows what might happen in the future, so it's good to have some experience in handling public disturbances and such.