I actually do disagree on one implication - you imply that the ratings of shows on other networks matters. While it's certainly true that a popular show can result in other shows in the time slot getting lower ratings (see Big Bang Theory vs. Community/30 Rock), the ranking itself doesn't matter. A show only has to compete against other shows on it's own network for a slot on the schedule - or statistically speaking for scripted shows, perform at or better than the scripted show average of a network. There are numerous examples, but they all boil down to the idea that if shows are performing strongly on different networks at the same time, all will be renewed regardless of inter-network ranking.
Rankings against other shows DO matter.
It affects advertising rates, first of all.
Second, relative ranking is ALWAYS taken into account when weighed against a network's other options- a show in a distant 3rd place (or worse) in its slot will be considered for movement to a new time slot to see if it will are better there. Or it may be supplanted in that slot by a higher ranked show the network thinks will outperform it in that slot.
It may face cancellation if the network thinks a new show will be a better investment...say, by a show with lower production costs, a big name star who should be a draw for the target demographic, or even a network executive's pet project.
Look at
Monk- a strong performer for USA, it struggled when ABC tried to add it to its own schedule and they gave up on it. And when NBC bought USA, they likewise tried airing the show on their network...where it floundered in fourth behind
Big Brother and some Oprah show and that experiment ended as well.
This despite outperforming
both ABC's and NBC's offerings in those respective time slots. In fact,
Monk's numbers marked a significant 23% increase in that slot for NBC. But it was still so low relative to the other shows the it got axed.