I'm afraid that's way too simplistic. You cannot hand over from one control system to another, either manually or "automatically" as you put it, unless and until you are sure that the secondary/standby system is working correctly.
There are two ways to look at it and I agree with what you are saying, don't get me wrong.. being simplistic to get an idea across, rather than get bogged down in the technicality of achieving it, if that makes sense. The idea can't be discounted until all angles of where it could go wrong are figured out, and fleshed out as to how it is managed and achieved technically..
If you have a major failure of all communication to an engine, and there was a 50/50 chance that the wireless would work, I think you would definitely want to have that 50% on your side. Even if it was a lesser percentage, something is better than nothing.
False positives are always difficult to figure out, but not to say that you couldn't figure out a way to cut the threat down, or at least investigate the idea without completely discounting it completely. It is the same as any system with any type of redundancy. One that comes to mind that, the wireless system has two stages of sanity checking, once where the live system picks up when a failure is recorded, and then another when a "go" live signal is received over the wireless to actually kick it in. A two part check, and part of it is figuring out whether or not the percentage of having both "false positives" at the same time.
As for advancement in technology, just look at where we have been and what has been achieved since. It is a continual improvement process, and as better ways of doing things are discovered they are applied. You of course can't deviate from physical real world limitations. Wireless technology will get better, and their reliability will increase as well.