Yes, Google Scholar is so useful and ubiquitous that it is dangerous. It would be far preferable to have a proper open replacement for it.
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.
The biggest problem with replacing google scholar is that if you are not google, publishers will threaten to sue you for crawling their website and/or displaying information about their papers on your website. If you are Google you can just counter-threaten to delist them and stop crawling their website entirely. Google is unfortunately one of the only players that can actually offer something like google scholar.
Harvard's ADS (http://adsabs.harvard.edu) has recently been revamped and is very effective in it's domain of (astro-)physics. Perhaps someone could base a Scholar replacement on that?
Google scholar has been updated a few times in the last 5 years. As someone that worked on a startup building an academic search engine and who is now a PhD student I am a pretty big fan of Google scholar. I to worry that alphabet will pull the plug.
