It seems to me, on the contrary, that transfer prices are going to go up.
Below, in the photo, you can see the stats: Transaction volume on BTC network, hits highest since September 2022 - The Block
Volume has no real connection to the average fee.
In fact volume can be really misleading in certain days because of what big players can do, for example: Binance can chose to move a part of it's hot wallet to the cold wallet and here you go, one small 170vbyte tx is worth 4 000 BTC.
Same for consolidations and mixing, if somebody decided to mix 10 BTC, then you have 10 from user to mixer, 10 btc from mixer to tumbler, 10 btc in coinjoin, 10 btc from coinjoin to mixer controlled addresses, 10 btc from mixer to user. And voila somebody cleaning 10 BTC has made an on chain volume of 50 BTC by effectively doing...not so much economic activity.
This is a better indicator for the fees:
https://mempool.space/graphs/mining/block-fee-rates#3dAnd only click on min excluding the others, but when you use longer periods it becomes messy and it stops showing the gaps, it's good for 24 and 3 days still.
[img heigth=200]https://www.talkimg.com/images/2024/02/07/vsSAJ.png[/img]
or use this:
https://bitinfocharts.com/comparison/bitcoin-median_transaction_fee.html#3m