Mizzou makes plenty of money through winning. They made more from the Big 12 over the past few years than they would have if money were divided evenly, actually. But the Big 12 contract is still crap.
Adding Missouri to the Big 10 isn't about the increase in actual TV audience. It's more about TV sets, period. The Big 10 gets money for every Big 10 Network subscriber (I believe it's 50 cents/month per subscription, but I could be wrong). If the Big 10 adds Missouri, that will cause Missouri cable and satellite providers to add the Big 10 Network to more standard packages. Adding just a few million more subscribers brings in tons of cash... 3,000,000 new subscribers = $18,000,000 annually from the state of Missouri... whether they're watching the Cardinals or the Tigers (the Rams, being an NFL team that plays on Sundays, isn't really an issue...).
I really don't think Mizzou's goal is to put pressure on the Big 12. Their goal is to join the Big 10. All the smoke around this isn't just coming from a few leaks on Mizzou's side. The Big 10 obviously wants to expand, and they obviously want to go past just 12 teams (unless the one addition is Notre Dame, and they don't join unless the Big 10 goes bigger than that). Missouri may not be the most attractive option for the Big 10, but they are within the top 5 IMO.