Just about every modern traction control uses fuel cut, not spark cut. Spark cut doesn't work very well at all on diesels, and pumping unburnt fuel straight through the engine and into a catalyst at 800deg on a petrol doesn't do much for its longevity. Older versions used to override the throttle but you cant get very accurate control using this method. Fuel economy actually improves when the t/c cuts in.
Direct injected engines (be they compression or spark ignition) can use fuel cut as the "fast path" torque reduction response because they don't have to account for the fuel "puddle mass" in the intake system (being directly injected). On a conventional port injected engine fuel cut is just about impossible under current emissions regs as you cannot accurately control the cylinders AFR during the cut transitions, which tends to lead to excess exhaust emissions(usually large NOx feedgas spikes due to lean and partial burns). A full spark cut however means you just dump a small mass of completely unburnt fuel out of the exhaust port, where it is oxidised by the catalyst at low enough temp and pressure (compared in combustion temps/pressures) that the formation of NOx is eliminated. For the couple of firing events before the "slow path" airside controller catches up, the heat release from this exotherm is not enough to damage the catalyst substrate due to over temperature.
On the DI engine, fuel is injected directly into the combustion chamber, so no intake system puddle mass exists, so you can control fuel mass without lead/lag, and hence torque on an firing event by event basis without issues with missfiring or partial burns, effectively you have two "fast paths" using spark retard to ramp out torque, and then a full fuel cut once you get to the retard limit.
It is correct that fuel economy improves, but only compared to the non intervention case. reducing the engines torque means it uses less fuel, but during these interventions the engines efficiency IS reduced (Specific torque output falls) so you are using more fuel compared to just running at the lower torque value without TCS torque reduction.
It should also be noted that TCS also can increase engine torque if/when required, for example to prevent the rear wheels "underspeeding" if a low gear is selected too early, or the driver agressively backs out of the throttle (or decending a steep hill etc), In this case, the TCS will ask for a "torque up" event to maintian mean wheel speeds and hence equalise tyre slip ratios.