Z, It looks like you are going for a very unique tea maker.
For the taste issues mentioned, a metal or plastic tea kettle is out.
So we are dealing with a ceramic or china pot, which do indeed "feel" like they will make tastier tea.
You will immerse from the top a device with both a heating coil and temperature sensor on it.
You'd do well to put as much distance between the two as possible, so you get temperature readings of the overall water, rather than of the heating coil vicinity.
Without a temperature sensor, and just trying to adjust the amount of heat ("tension") may be problematic.
You will have to account for differences in the amount of water and the thermal capacity and heat loss characteristics of the container.
One setting of "tension" will not work well for both 1 cup and 1 liter, or for both a metal and a ceramic pot.
So therefore you should have a temperature sensor involved in the control of heating, not just for display of current temperature.
Now we are left just with the question of relay, as everybody including me prefers, versus variable heat, as you are enamored with. 
Let me add this tidbit to the argument for full On/Off, i.e relay control, other than that it is easier and safer (which it is).
Did you ever do the experiment of heating a water balloon to boiling over a candle flame?
It works. All the time. The water averages the heat going in, never letting the balloon temperature get higher than the water temperature.
I think a similar thing will happen if you go through the trouble of putting pulses of heat or even variable voltage to the heater.
No one will know. The water will only take more time to get to the desired temperature.
Additional problem if you are operating "open loop", i.e. without a temperature sensor as part of the control - once the water has slowly reached the temperature you want, there is nothing to stop it from increasing further since heat, even at a partial setting, is still still being applied. (Yes, there will be some difficult-to-determine equilibrium temperature it rests at)
If, after all this, you are still convinced you want adjustable heating, i.e. no relay, then make that visible to the user.
Give your user interface an additional parameter to "Temperature setting".
For example "Maximum heating rate (1-10)", or "Heater power (1-10)", or even "Slow cook enhancement(1-10)"
What are your thoughts now about this? Relay or no relay? Start with relay and add PWM later?
Additional aesthetic note: The PWM approach is elegantly quiet. The relay will make repeated clacking as it maintains a temperature!
Best!
Techylah