Why temperature is the thing worth controlling
Bitter compounds extract faster in hotter water than sweet and savoury ones, so a delicate green tea brewed at boiling gives you the harsh part efficiently and the pleasant part poorly. This is why so much green tea tastes bitter and thin at the same time, and it is a temperature problem rather than a tea problem. Getting this right is worth more than any equipment upgrade.
Doing it without buying anything
Boiled water left standing in an open jug drops quickly at first — a few minutes puts you in green-tea range in most kitchens. Pouring between two vessels drops it faster and is easy to repeat consistently. Adding a measured splash of cold water is the most controllable of the three: roughly one part cold to four parts boiling takes you from 100 °C to about 85 °C. None of this needs to be precise; being deliberately below boiling is most of the benefit.
What a variable kettle buys you
Repeatability and not thinking about it. If you brew green or white tea daily, that convenience is real and compounds. If you mostly drink black tea, dark tea or roasted oolong — all of which want full boiling water — it buys you nothing at all, and this is worth knowing before spending.
Gooseneck spouts and other refinements
A narrow spout gives a slow controlled pour, which matters for whisked matcha and for pouring gently onto delicate leaf. It does not change extraction in a Western mug. It is a comfort feature, which is a perfectly good reason to want one and not a flavour argument.