To actually reduce engine thrust to zero would require in-flight shutdown of all engines. As already discussed, this isn't done for a variety of reasons; one such reason is the use of bleed air, and another is that starting the engines is a multi-step process that can take some time even without the complexities of starting an engine that is windmilling rather than at a standstill, and a third is that engines provide more than thrust (such as hydraulic pressure or electricity for non-critical but still useful systems, including additional radios). Shutting down all engines in flight is something you really don't want to do, because doing so deprives the pilot of options; for example, it makes a go-around or even just handling an unexpected gust of wind far more involved than it needs to be.
What is often done, however, is to reduce thrust to idle. Idle thrust does not mean zero thrust; idle thrust generally means some low amount of thrust above the minimum required to keep the engine safely running (which itself is typically non-zero). Because the engines are still running, it's a relatively simple process to increase thrust if needed, which means that unexpected events during the descent can be dealt with much more rapidly and safely.
There are other ways to descend. The pilot could simply point the nose towards the ground and leave the engines where they are (assuming no autothrottle or similar system), but that will cause speed to increase. In light motor aircraft, it's probably pretty common to compensate for this by simply reducing engine thrust along with pitching the aircraft down, unless you actually want to descend under power.
Another option, which is probably more common on large aircraft, is to deploy high-drag devices such as spoilers or air brakes without a corresponding increase in engine thrust.
Remember that the aircraft can be treated as an energy system with fuel burn (controlled by the thrust levers) providing energy input, lift helping keep the aircraft in the air, and gravity and drag costing energy (in different directions; typically downward and forward, respectively). If you increase drag, for example by deploying high-drag devices, then basically one of two things will happen: (1) the drag of the aircraft increases (duh) which means that if you were previously in an equilibrium, you are now "spending" more energy than you have available, causing either a descent, a reduction of airspeed, or both; or (2) you will need to increase thrust to compensate for the increased drag to maintain speed and altitude. (#2, by the way, is why the landing gear is retracted early during the climb-out; doing so reduces drag, leaving you with more power for climb.)
An effect of #1 is that you can control the pitch of the aircraft to choose how much the speed changes, and how much the altitude changes. (Airspeed and vertical speed, respectively.) The pilot (or autopilot) can simply pitch the aircraft to maintain a desired airspeed and let the vertical speed become what it may, or they can target a vertical speed by pitching for that and simply monitoring the airspeed to make sure they aren't overstressing the airframe on the high side, or approach the stall speed for the current configuration on the low side.
All in all, airplane pilots have lots more options than car drivers (and the above doesn't try to provide an exhaustive list), but something exactly resembling "neutral" in a car isn't one of them.