First off Gandalf's plan was to have the nine companions venture into mordor. Also your nifty plan is even less likely to work than Gandalf's plan. There are many problems. What if the rat misses? What if it wisely decides not to crawl into the hot lava? What if possibly an aerial attack would catch Saurons eye? That is what gandalf was trying to avoid. Then as your eagles are flying over Mt. Doom Sauron will steal back what is his and there goes the whole quest. On the whole your analysis was ok but your plan didn't take into account all of the things gandalf's did.
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First off Gandalf's plan was to have the nine companions venture into mordor. Also your nifty plan is even less likely to work than Gandalf's plan. There are many problems. What if the rat misses? What if it wisely decides not to crawl into the hot lava? What if possibly an aerial attack would catch Saurons eye? That is what gandalf was trying to avoid. Then as your eagles are flying over Mt. Doom Sauron will steal back what is his and there goes the whole quest. On the whole your analysis was ok but your plan didn't take into account all of the things gandalf's did.