Isn't it possible today to make a down-transformer without coils, without the idea of induction? After all, the AC reaches every voltage in-between, so all we have to do is keep cutting the power flow and only letting current pass when the wave is at the desired voltage. Of course, this will be a series of pulses but it can be smoothed out with capacitors.
All of the methods involving motor/generators or cycloconverters are still going to have coils and induction, so do not fit the OPs desired solution.
But as alluded to, it can be done electronically with high speed solid state switches, as long as you only want to REDUCE the AC voltage. Do a search on "Phase Angle Voltage Control" for details that are too long to post here. But in a nutshell, that's exactly what it does, delays the firing of a thyristor (SCR) so that only a portion of each sine wave gets through and results in a lowering of the RMS voltage. The main difference however is this; in an electronic voltage controller, the CURRENT on the output will be the SAME as the current on the input, just at a lower voltage, so the POWER is LOWER. With a transformer, the current on one side it DIFFERENT from the current on the other side by the ratio of the windings (inverse of the voltage change), so the POWER is the SAME . There are losses involved in both methods, so for simplicity, call them the same.
The capacitor method, also called a "voltage doubler" circuit works too, but only if the desired output is DC, plus becomes incredibly cost prohibitive compared to transformers in higher power levels.
Is it possible to make a step-down CIRCUIT without coils?
Sure, we typically call them "lamp dimmers" or "motor speed controls", etc. etc. There are millions of examples all over the globe. There may be one within a few meters of where you are right now.
Is it possible to make a (whatever) TRANSFORMER without coils?
No. By definition a transformer (in the ordinary sense) is made with one or more windings ("coils" if you will).
Sure is possible. What you want is a cycloconverter. Overview of cycloconverters
Yes, it's possible to do that with an electronic switch that opens once the input AC voltage exceeds the desired output voltage, on each cycle or half-cycle depending on whether the input is half-wave or full-wave rectified. This Design Ideas article illustrates a method using only discrete components.
No coils needed, but the input does have to be something like a sinusoid (no square waves). With square wave input the pass device would have similar losses to a linear regulator, while causing a lot more EMI.
It does not have very widely useful applications because it puts a lot of harmonics into the input power, but it does work nicely and losses are not necessarily high (the peak current is higher than that of an equivalent rectifier-capacitor filter because the input voltage is higher so the dv/dt is higher) .
There are 2 kinds of reactive transformers. Inductive and Capacitive.
But an R divider is Not a transformer.
This is the most common high voltage transformer for low power.
Then we have R1/R2 dividers and PWM open close switches where the shunt R2 n series with PWM toggle between R2 and open cct thus R2'=R2/%d.c.
... or Triac Phase controlled switches which are similar to PWM but at line rate.
---- then there are motor / generators which can transform both voltage and frequency in ratios.
However the most popular practice today is to step up AC to higher DC with active PFC then DC-DC to step down with inductors in stead of use heavy bulky expensive cold-rolled grain oriented laminated steel core transformers for step down DC converters. This method has become mandatory in the EU for PSU"s >100W due to the THD overload of distribution transformers neutral wire harmonic currents from too many poor power factor rectified line caps.