I mention the whole existing situation when America went to war, that this was a matter for joint diplomatic action with Russia. Clinton passed on Rwanda when the slaughter of innocents was far worse and the solution much simpler, just send in a battalion and show the flag and they could have done that through the UN. Serbia was a rush to war with no clear goals as in Iraq and an improvised ending, the independence of Kosovo, which could haunt the world for generations.
You' missing some of the main points as to why the US went to war, i.e. NATO and what had happened previously in Bosnia (not so much Rwanda).
More specifically, the main reason NATO found itself sucked into the the Kosovo conflict was because there was a prevailing belief - at that time - that if the conflict was not stopped, it would soon spill over in Macedonia.
If that happened then that republic's neighbors would be brought in. Albania would invoke its defense treaties with Turkey, Greece would then become involved and there were worries that there might be repercussions in Cyprus.
As such, it was thought that it might be better to become involved too early then too late.
Another point I would make, is that the NATO bombings were a (knee-jerk) reaction to Serbian actions from Dubrovnik to Vukovar, to Sarajevo, to Srebrenica - as I mentioned above.