I think also another reason for such needed secrecy was for the safety of Rivendell.
Most of the Elves were leaving, and eventhough Rivendell had some formidable warriors, it wasn't a place that could muster up an army like in Lorien or Mirkwood. Rivendell was more of a refuge and a safe haven for people to go and get Council. It was a hidden place for refuge, not a place right out in the open that could gather an army and stop assaults. It's remained secrecy was a must.
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1697: Eregion laid waste. Death of Celebrimbor. The gates of Moria are shut. Elrond retreats with remnant of the Noldor and founds the refuge of Imladris.~Appendix B: Tale of Years
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It was founded by Elrond as a place where the remaining Noldor retreated to and could go to and created as a refuge.
We also see times where Elrond has to go to other places to muster up an army, as Rivendell just doesn't have the people:
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"It is said that Angmar was for a time subdued by the Elvenfolk coming from Lindon; and from Rivendell, for Elrond brought help over the Mountains out of Lórien."~Appendix A: Of Eriador, Arnor, and the Heirs of Isildur.
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The safety of Rivendell was dependent on it's secrecy to the Enemy, it wasn't a military powerhouse (though it was a place with several good warriors) that could withstand continuous assaults. So, I'm thinking that Elrond didn't want to risk the secrecy being lost, as Rivendell simply didn't have the manpower (err...Elven power) to withstand attacks if it's exact location was found out.