I think that by the time that Google is able to quantify quality and relevance, people will be able to use AI to automatically create websites that are relevant and high quality.
I'm not sure whether that is a good thing or not, but it would make sense that the sophistication of the AI used to game Google moves at about the same pace of Google's ability to stop people from gaming its algorithms.
I suspect it's not that hard to get a very rough assessment of quality and relevance - although it would only be useful with a giant multidimensional model of demographics and interests, because "relevant" isn't a scalar.
My guess is Google doesn't do it because it costs too many cycles. Counting backlinks, supplemented by some very basic NLP, is very much cheaper and easier.
The irony is that I wonder if people would pay for - or at least not mind - guided and prompted personal search if it produced highly relevant results.
The sad truth is that the current sneaky lumping of broad demographic guessing with search history with backlink counting and a bit of NLP/timeline voodoo produces mediocre results for many kinds of searches. (I've just spent a very frustrating 15 minutes trying to find out if the raw datasets from KIC 8462852 are available online. Usually my search fu is pretty good, but I couldn't get a definitive answer.)
I'm not sure to what extent Google's sales model relies on this. It's much easier to sell advertising if you don't offer an SLA, because it becomes the customer's fault if the service doesn't provide high quality results.
A more effective service would increase ad buyer confidence and the price of niche ad sales would increase, but maybe not by enough to compensate for the loss of more generic ad sales overall.
I'm not sure whether that is a good thing or not, but it would make sense that the sophistication of the AI used to game Google moves at about the same pace of Google's ability to stop people from gaming its algorithms.