Hello Charlix, welcome to the forum.
We all know that allowing misinformation to be repeated is the stuff that turns myths into legends right? Well, this is the only reason I'm going to hit on this topic that has been discussed many, many times already.
As for the car analogy, that is what a closed loop O2 sensor does, it looks for changes in the fueling so it can feed back to the engine controller and trim for fuel changes, small air leaks, and a whole host of other things that are correctable by software for a small hardware issue which will occur on every car eventually. That seems a lot closer to backlash than a loose steering wheel.
This is where you are dead wrong. While your analogy of an O2 sensor is fairly accurate the only way it can work properly is if it has full control of all elements involved. Should the ECM decide the mixture is a little rich and needs to adjust the air/fuel ratio by lowering the pulse width of the injector. It does so but the actual time the injector is open for does not actually change because there is a piece of trash in the injector keeping it open. This is something the ECM assumes it has control of but actually does not. What now? How does the ECM fix something it has no control over? Does it cut off the fuel pump to lean it down resulting in starving the engine for fuel and ultimately shutting it down? Does it inject air to adjust the A/F ratio and in the process raise the RPM of the engine? Do you add a pile of telemetry sensors and mood recognition to read the environment and drivers face so you can take all of that information to make an educated decision about what is the best option? These things and lots of others could be done to compensate but at what cost and what sense does it make to even try to. The best possible outcome would be piss poor at best.
You can avoid reality but you cannot avoid the consequences of avoiding reality.
Mach3 does have backlash comp. that works as good as any but I wouldn't get Mach3 or Mach4 or any other controller expecting it to be able to fix all the woes introduced with backlash. If I knew of one that could manipulate physics I would sure point you to it.