Think of the Floo network as a set of roads, rather than an information network. On the internet you send a packet of information down a wire to a node, which then resends it to the next location, based on one of the topographies provided in the original post. In such a case, you have to worry about the integrity of the nodes and how they handle the information. But a road network is different, although it is similar to the "internet" graph. Rather than having nodes, you have intersections. There's nothing between you and your destination but the pathway. The downside, though, is that the traveller must be in control of its pathing, wether that's you, your driver, or the floo powder swirling around you. The intersections make no decisions, they simply exist.
Now in the floo network, it is described as Harry passing by several fireplaces and catching glimpses of what's through them. These glimpses can be confirmed as normal because, in The Cursed Child, Ron mentions seeing Albus and Scorpius with Delphini while he was going through the Floo. As such, these glimpses would be akin to seeing houses while driving down the street. Adding or removing a fireplace would have as much effect on the Floo network as building or demolishing a house along the road. It doesn't affect the path, only the availability of the end point.
As for ministry control over the Floo network, this would be analgous to your local government's control over public roads. They build and maintain whatever it is that you travel along.
Finally, it seems likely that wizards would have built on the concepts of roads, since there is such a long and rich history of such pathways, rather than information networks which are a rather recent discovery.