This is absolutely not correct.

Award pricing is influenced by the current cash fares.

If you cannot currently "buy" an award ticket at the old rate, your cancelling your existing booking will, in most circumstances, NOT lead to a new ticket being made available again at the old rate.

The closer you are to departure - when all the cheap cash fares with advance purchase requirements are no longer available for your travel date - the more this applies.

There is even no guarantee that cancelling an award ticket will lead to a new award seat being opened on all flight(s) thus released - particularly if the flight is close to departure and it is oversold or where the only remaining cash tickets are only available in the most restrictive fare classes