The '3 or at most 7' note was not CT's work, but JRRT's.
Three does work if we consider that Tolkien may have actually been toying with an idea that would leave only those three that we have specific accounts of: Gothmog, Glorfindel's Bane, and the Durin's Bane. He may have planned to implement this radical reduction at some point in the future. Perhaps all of the Balrogs in the Fall of Gondolin (besides Gothmog and Glorfindel's Bane, and no doubt Durin's Bane, though he wasn't specifically mentioned), the Nirnaeth, the War of Wrath, and any other mentions, would have been replaced with Boldogs or Trolls.
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