Google scholar should filter out self citations. Google scholar hasn’t been updated in like 10 years I sometimes worry alphabet will pull it’s plug.
The technical issues are probably "easy". The ongoing maintenance costs/hassles could be solved. But the human factors would be very tricky to get right: anyone who maintained it would be under a lot of pressure in their decision-making -- your example of whether self-citations should be filtered is a good example of a decision which would have big effects and would be highly political.
One good thing about Google Scholar is (was?) that we didn't worry that Google engineers would tweak it to benefit Google researchers.