From
The Letters of JRR Tolkien, in a letter to Naomi Mitchison (letter 144) who had been reading page proofs of FOTR, in reference to the
Balrog, Tolkien writes: "The Balrog is a survivor from
The Silmarillion and the legends of the
First Age. .... They were supposed to have all been destroyed in the overthrow of Thanggorodrim, ..... It is observable that only the
Elf knows what the thing is -- and doubtless
Gandalf." The elf referred to is clearly
Legolas. So here you have Tolkien essentially stating that
Gimli, though he identifies the creature as "
Durin's Bane" does not know what it truly is, only Legolas and Gandalf recognize it as a Balrog. Therefore in Tolkien's conception of the story the
dwarves either never reported Durin's Bane with enough detail to identify it as a Balrog, or if they did the identification was never passed back to the dwarves (or certainly not to Gimli). Is the argument now that the
elves and Gandalf knew that Durin's Bane was a Balrog, but never told the dwarves? Why would they not tell the dwarves? If Gandalf knew that Durin's Bane was in reality a Balrog, wouldn't he on hearing about
Balin's attempt to reopen
Moria say something along the lines of: "Are you crazy! There is a Balrog in there! Let sleeping
Balrogs lie!" (The same could be said for
Elrond if he knew the identity of Durin's Bane. Perhaps even a "This is a job for
Glorfindel!

)
As for the argument that Balrogs were known from
tales of the earlier
ages,
Aragorn, who Gandalf calls the greatest traveller of his Age (if I remember correctly) also does not recognize the creature they are confronted with as a Balrog. In addition to Tolkien's statement above, we have in FOTR when the Fellowship first meet
Celeborn and
Galadriel in
Lothlorien and report Gandalf's fall, Aragorn says: "An
evil of the Ancient World it seemed, such as I have never seen before. It was both a shadow and a flame, strong and terrible." Not only has Aragorn not seen a Balrog before, but he clearly did not know what it was other than guessing it was an ancient evil. It is Legolas who identifies it to Celeborn and Galadriel: " 'It was a
Balrog of Morgoth,' said Legolas". Also, if Gandalf knew that Durin's Bane was a Balrog, wouldn't he have clued in Aragorn? Thus all the evidence (both internal in the story and Tolkien's own statement) is that it was not known that Durin's Bane was a Balrog.
As to the argument that Gandalf and
the wise should have guessed that Durin's Bane was a Balrog, why should they? All the Balrogs were thought to be destroyed ages ago (

). If reports came in from the American West about slaughtered cattle, I don't think anyone would consider
Tyrannosaurus rex as a possible culprit, no matter what any eyewitnesses might describe.