The problem with noise seems to be repeatability. Enough noise, and reliability becomes a huge problem. With same inputs and analog circuit, you want the same answer every time, don't you?
You cannot "overcome this noise" by removing it. The perfection of materials, process and environment required for that would be on the order of an experiment like this: https://www.simonsfoundation.org/quanta/20131010-neutrino-ex...
We overcame the noise via digitization. In fact, there is obviously still noise in our current digital computers, since the components within them are fundamentally analog, but digital circuits quantize the analog signals, interpreting the 1's and 0's, despite their analog nature. (this is simplified and I know next to nothing about digital circuit design)