If the eagles had flown him, none of those factors would be at play. Frodo could have still had the strength to overcome the ring's power and throw it into the fires.
My understanding has always been that Gandalf alone understood this and necessarily was hushed about it or otherwise it would have totally destroyed morale. He let others believe it was possible to willfully destroy the ring when in fact it was not.
Gandalf was said to be the wisest of all of the Maiar. So if he had a feeling that Gollum would have a role to play, it was probably worthwhile allowing Gollum to play that role. I have no doubt that Gandalf knew that Frodo would falter at the end.
I guess it comes down to the following factors that might have an effect on ring-resistance:
- strength of character/will
- strength of body
- proximity to Sauron