It is not that because Bitcoin's value rises and so the fee will increase as well. Fees depend on the number of transactions being made like now Bitcoin having expensive fees because there's a lot of people are now buying Bitcoin to enter with the trend and some are selling because they made an exit. Hence, it is not true that when a coin rises and so the fee it can also happen when a coin when it plummets because everyone will tend to accumulate. But if you want to reduce that fee there are few solutions like using a Bitcoin lightning network or try using a Native Segwit address or bech32.