Good guys of LOTR clueless?

[Maédhros]

Yes. There can be no doubt about it. Both the passage that Earendilyon quoted and that which I quoted distinguish the lesser rings, which Gandalf describes as trifles for Elves but dangerous to mortals, from the twenty Rings of Power, ie the Three, the Seven, the Nine plus the One Ring, which he describes as perilous. It is clear from this that the Elf-smiths of Eregion created rings other than the Rings of Power. And the word "many" combined with the reference to them being "essays in ring craft" strongly suggests to me that there were quite a number of these lesser rings.

Yes, I have to agree with that. I thank you for showing me that. Nevertheless, this same fact make the good guys all the more incompetent.
Consider:

1. Gandalf felt uneasy about Bilbo's ring.
2. Gandalf knew that both rings had similar descriptions 11 years after Bilbo returned to the Shire in the White council discussion.
3. Gandalf while in that council mistrusted Saruman as to not tell him about Bilbo's ring but was satisfied about his conclusions that the ring could not be found.
4. In a world where gut feelings are as important of more important than common sense then was Gandalf not following his feeling odd?
5. If they were m lesser rings, what was the probability that Bilbo's ring was Sauron's? P=1/(m+1). Where m = the amount of total lesser rings. If m is big number, then the probability decreases.

With all those facts, do you really think that it deserved an investigation?

Lets look at what Gandalf did. He thought that m was a big number so that the probability of Bilbo's ring being Sauron's was almost nil.

It is in the year 3001 TA that Gandalf suspects that Bilbo's ring can be that of Sauron. What if Bilbo's ring turned out not to be that of Sauron, what could the good guys have done to defeat Sauron at so late a date in the TA? What was the plan? Did they even have any?
Could they overthrow Sauron by force of Arms? No.
What in Gods name would they have done if they had not found the One Ring?