In a certain sense, there are two different questions here. One question is about the need for a variable temp. kettle. The other is a question of the importance of water temperature in brewing tea.
You certainly do not need a variable temp. kettle. For most of my tea brewing life I did not own one. You can simply heat your water with an ear for the music of the boil, using a stove with a stainless, glazed or unglazed ceramic kettle, or a glass kettle. Or, you can use a cheap Aroma, portable, plug-in type kettle that only boils water. So, in this regard you don't need a variable temp. kettle; nor do you really need a thermometer. Though both can be useful.
In regards to water and identifying your heat:
Lu Yu: " Of boiling, when the boiling water is like fish eyes, and there is a slight noise, this is the first boil. When on the edges it is like a surging spring and joined pearls, this is the second boil. When the water is surging and swelling waves (rolling boil) this is the third boil. Anything after this, the water is old and cannot be drunk."
XuBo: "The ancients boiled tea as poems were copied and written about heating the water; each had exquisite skill. Pi Ri Xiu's poem says: "Now and then see crab eyes splash. I see suddenly fish scales (ripples) arise." Su Zi Zhan's poem says: "When crab eyes already passed fish eyes are born, whishing on the verge of making pine winds sound." Su Zi You's poems says: "When the copper cauldron attains fire, earthworms call." Li Nan Jin's poem says: "Crickets chirping, ten thousand cicadas hurrying." Imagining this scenery, a gentle breeze arises (one attains a state of lightness and elation)."
Chen Jian's Ammendments To Lu Yu:"In the degree of boiling water, the commencement is called shrimp eyes; next is called fish eyes. The water boils to the point where one hears as though pine wind's sound, and gradually become no sound. [Note: Shrimp, crab, fish eyes are said to be the internal form of boiling water. When the the water sounds like pines soughing in the winds to the sound gradually slowing, then the degree of fire has arrived! Past this point then the water becomes old (over-boiled).]"
Su Yi Zhuan: "Hot water controls the destiny of tea: if famous tea is added to excessive hot water; then with ordinary, coarse tea there is no difference. Therefore in boiling hot water there is the old (over-boiled) and the tender (under-boiled); in pouring, there is slow and fast; not past either extreme are the limits of tea."
Quality of water and the proper heat absolutely are important. At one phase in my tea drinking I spent about 6 weeks of tea brewing time just drinking and brewing water only (no tea) from different sources (store bought, plastic bottled, glass bottled, natural spring sourced, Sierra creek water, Brita filtered, Shacklee filtered, water stored in iron, gathered and filtered rain water, snow melt water, etc.) in various vessels (different teapots, different cups (glazed/unglazed, etc.))to really discern the difference and effect of various water in combination with different heating and drinking vessels. This was an absolutely important phase of my tea drinking.
I will also have to disagree with miig. While it is possible to brew other teas besides sensitive greens with only boiling or slightly off-boiling water there is a lot one is missing in their tea with such a generalized approach. I listen to each tea differently; I don't brew by which class of tea a tea leaf happens to be categorized in; that is only the starting point. Brewing an wulong tea at 90 degrees Celsius will elicit different outcomes from the same leaf than if brewed at boiling temp. In fact, I don't even brew a single session of tea at the same temperature most of the time. During a session of tea I will vary my temperature in harmony with what the leaves are telling me or to get more rounds or more flavor out of a pour, etc. I might start a pour at 90 degrees Celsius and finish my last round at 98 degrees Celsius. I typically pour my second round cooler than my first because the leaves have been heated and opened. If I am not using a variable temp. kettle or thermometer then I am varying my temp. by how long I let the kettle sit after removing it from the heat source or what height I am pouring my water from, or both.
There are many possible outcomes within the alchemy of tea and one is missing a lot of nuance if they are being cavalier with their water heat in regards to a certain tea. That said, tea and water don't have
to be given this amount of attention to just enjoy
a cup of tea. But paying attention to one's kettle/water temp., water quality (source, ph, minerality, etc), brewing vessel, steep times, specific leaf choice and amount, cup choice in combination with a pot (ex. Yixing clay pot poured into glazed cups will yield different results, mouthfeel than Yixing clay pot tea poured into an unglazed earthenware cup, etc.), visual aesthetic harmony, etc. is the beginning of the art of tea and not just tea drinking. For me, participating in this alchemy is not only one way to honor the leaf I drink and the time I take to sit for a pour, but also a way participating in the truths of impermanence and fluctuation inherent in the created order/universe. I don't see an end to the rabbit hole and with greater receptivity, sensitivity, and presence I find my tea times have become spaces that any descriptors fail to fully encapsulate. But again, paradoxically so, it's just tea...and it can be many things for many people. It can be as simple or complex as you want it to be.
In the tea room I use the Bonavita Gooseneck variable temp. kettle. It is convenient, highly adjustable, and reliable. A temp. can be held or adjusted through the ease of pushing a button. This kettle has been discussed throughout the forum. Here is one such spot: (viewtopic.php?f=36&t=19345&p=254282&hilit=variable+temp+kettle#p254282
However I also have two silver kettles, an iron tetsubin, two different clay kettles, and two stove-safe glass kettles, each with their own effect on water/tea. I also have a setup in the tea room to brew over coals that I only in December finished making/gathering together. In Taiwan, while practicing tea with my teacher, we almost always brewed over coals but it is something that needs the right space and time to prepare: