Regulating high voltage high current ac supply
'Normal rectifiers' are indeed available at such voltages. You'll actually need to use 'fast' rectifiers in an SMPS though.
You appear to be talking of a line frequency power supply though. No problem really. Just ensure your transformer is suitably rated. For 2kW DC load, you should typically use a 3,6kVA transformer for safety (not overheating due to harmonics/conduction period related issues). Also the same for the variac. How tightly regulated does the 400V need to be ? That'll be the issue. Do you need help with the ripple calculations, esp voltage ?
Why would you need huge capacitors ? Energy storage at high voltages makes better use of CV  product (which relates to capacitor size) than at lower voltages. Energy stored = 1/2.C.V^2 , meaning that storage caps are 10 times more effective volumetrically than at 40V for example.