I would not agree that Eru directly intervened during the Third Age; that's seems a bit overkill. He could have jumped in the game many times during the 'Morgoth years,' yet did so only rarely. When he did intervene, it was for some big thing like changing the layout of Arda.
Just what does divine intervention mean in regards to free will and playing by the rules? Manwe et al should have let Arda burn as eventually Eru would have
had to jump in. What does this mean in regards to faith and personal responsibility? If I can force the hand of Eru ("here Sauron, here's your Ring back...okay Eru, do your stuff"!), what does this say about Eru's status/power? And what faith do I need if I know that Eru will only let the game go so far before joining in to catch me up. Was then Melkor right to oppose this thinking? How can one grow if not tested to the limit? I have to 'do my job' as I'm never sure if the eagles are coming or not.
Did not the Valar, who could have easily defeated Sauron, send the Istari so that they would not have to get involved directly? Wasn't that one of the problems with the Elves (direct intervention) where good intentions led to a lot of strife? Eru/Manwe/something may have
at most nudged things along a bit, but that would be the extent of 'divine intervention.' Could Eru's intervention be the creation of Hobbits, of which two end up taking down Sauron?
Gandalf, of the same kind as Sauron, was permitted only to use his powers when absolutely necessary - as stated previously, usually to allow for fair game play (Gandalf the referee?

) - yet I guess that Eru can have free rein in ME (then again, it's his so...). Saruman was a contender for the seat, yet was destroyed by beings of ME, not Valar nor Eru.
Also, to presume Eru's intervention diminishes the roles/sacrifices of Frodo et al.