1-TMC is before everything a French channel owned by the French broadcaster TF1 for 80% and by the State of Monaco for 20%. The channel TMC itself isn't very rich, but it can easily afford it. It's the 5th channel in France in terms of rating.
2-The broadcaster TMC has always expressed their disinterest in Eurovision Song Contest, as much as TF1's one. It has also no interest to have two broadcastings of Eurovision in France. It would attract no audience to broadcast exactly the same thing as France 2. It has happened in 2005 and 2006 (2004, TMC wasn't available in France yet). Apparently, TMC did a San Marino in 2004/5/6 letting one producer, Phil Bosco, entering Eurovision in the name of Monaco with his own songs and chosen artists. As results were very bad, TMC decided to let it go.
3-The State of Monaco has absolutely zero interest in entering Eurovision. It doesn't need it to have publicy and has already worldwide attention in organizing everything it wants. And the prince is found of sports, I don't believe he's a Eurovision fan !
4-Monaco still uses EBU to report the events of the principalty such as the wedding of Albert and Charlene...