Our compatibility specialists double-checked "CURCY - WooCommerce Multi Currency Premium" and they are using a cookie to store the currency information. This is the same workaround applied on your site and that is the reason why it is working 🙂
Curcy has a setting "auto detect". Setting it to "no", it will not set cookie at the first page load and deliver the default currency. Then it can hit cache at FIRST PAGE load.
Yours will always set cookie at first page load, so visitor will miss cache at first page load, and in subsequent page, it will hit cache. However, first page load speed often decides a site's bounce rate.
My server is litespeed, 16GB ram, 320GB storage. With WPML, it would take 3~5s to open the first page if miss cache. It's the line of sucess and failure. I think you should fix this so that we have a quicker first page load.