When I see someone want to get high voltage - we see tesla coil.
Why everyone do that instead of building Cockcroft–Walton generator? Are there any issues with Cockcroft–Walton generator, making it less fun than tesla coil?
It's more fun. Nothing says "mad scientist" like big coils, a few jacob's ladders around the place, sparks flying off towards the sky, and a visible corona. Some of these things don't work with DC, and a few diodes and capacitors aren't nearly as awe inspiring.
Mostly, the tesla coil is simpler than the multiplier. If you want to increase the output voltage of the CW generator, you need to inncrease the number of stages and/or voltage tolerance of the diodes. If you want to do the same for the tesla coil, simply use a bigger coil.
The way I understand it, a CW Generator creates high voltage DC, whereas a tesla coil create high voltage AC.
For the fun sparky effects it is easier to use AC that DC as it should spark at a lower voltage.
Also, to get a CW generator up to the kind of voltages that a tesla coil typically gets to (say half a million volts) would take a lot of stages and be quite hard to make.
Maybe it's the added bonus that the Tesla coil makes lots of noise. The old school spark-gap ones buzz rather loudly, and it's even possible with solid state drive to make a TC emit audio signals from the discharge.
A tesla coil uses resonance ,and the q of the secondary multiplies the reactive watts. The reactive output of a tesla coil at 500kv at 8 amps is 4 Mega Watts. Though its not true power ,what your seeing is the reactive power entering the capacitance of air. A voltage multiplier is just true power being stored and discharged.
Tesla Coils are marginally less dangerous due to the "Skin Effect" whereas a C.W. Multiplier can become deadly pretty quickly. Also, having a constant stream of arcs, that loud buzz, and the smell of ozone is an experience that a Tesla Coil is quite adept at providing! Besides, a Tesla Coil looks a lot like the universally recognized "Ray Gun"!