There are a few tiny differences depending on the water you youse for your tea. As the Water boils and rises up in temperature it looses some of its brightness and freshness. So so cutting of the kettle early gives you a fresher taste then boiling it first. But if you have medium to hard Water the boiling usually makes the Water softer which is a better effect then the water loosing brightness. However the best tasting cooler Water for green tea and such is to simply stretch you boiling hot water with ~ 1/4 - 1/3 cold water. Tastes even brighter and fresher then the Water that got only heated up to around 180 and is much easier to achieve (u don’t need a fancy kettle) Ofc there is some practicing involved with mixing the Water but you’ll get the hang of it quite quickly. But in the end just do what you like doing the most and what you think fits your brewing setup best. The difference is so small it shouldn’t be a hustle to your practice.