"Blindly" following TCAS guidance is no different to "blindly" following windshear escape guidance, or flight director guidance in autoland, or any of a number of other cases. Yes, there may be one chance in a billion that the systems have gone u/s and are giving you misleading guidance. That's the defined certification risk, after all. But there's a great deal more than one chance in a billion that someone doing their own thing by the seat of their pants will, in fact, do the wrong thing (or a worse thing) and will create more trouble than they were in to start with.
Is the TCAS RA the optimum solution to every single encounter? No, but it's a reliable solution.
Just as in the brakes case: is the anti-skid the very best you can get? No. Maybe you can beat it by a few %. But if you try to do so, you may also screw it up and fail by more than a few %. Now, if your ALD and LFL were based on "the box", there's no upside in being a couple of hundred feet short - and a huge downside in being long, if the runway is limiting.
The entire system is set up on the assumption that the person sat in the left seat is not an expert - there's a huge community behind the procedures, some of whom are experts. Following the advice of the experts, as encompassed in SOPs, is rarely a bad idea.