Agreed, a single IC alone won't handle 6kW, but ICs are perfectly capable driving external switch devices such as MOSFETs or IGBTs, which are capable of handling >100kW. These give a minimal component count for the controller by integrating all the 'intelligence', level-shifting, and isolation on one IC.
International Rectifier's website has details of numerous driver ICs for IGBT and MOSFET control schemes. It might be worth a look, although I don't recall any IC specifcally for your purpose.
Scotty.