Wikipedia Equality can be done. But we need to start the discussion
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Wikipedia is actually falling victim to the opposite: ideological tyranny imposed by a small cadre of editors.
Some Wikipedia articles now show noticeable bias (e.g. compare the "Men's Rights 'movement'" article to "Women's Rights"). On many pages, particularly gender related articles, there is a band of aggressive editors who will fight reasonable efforts to balance the tone of articles. Outside contributors who try to improve these pages will get dogpiled on. Unless you are an expert at wiki-lawyering, you won't survive even a couple edits before you are banned or restricted from editing. They enforce/investigate multiple accounts, VPN & proxy usage vigorously, so once you are out, you are effectively purged. If you are ambitious and make edits similar to what others have tried (often because all of them are trying to fix the same biased statement), expect to be accused of being a "sockpuppet" or of being a "meatpuppet." If that fails, you will be accused of "tendentious editing". Of course responding to these accusations takes extraordinary amounts of time -- which is the point. These tactics are used (very successfully) to reduce people's resolve to contribute or fix biased articles.
Wikipedia's ideological hijacking is a serious problem and arguably represents the biggest threat to Wikipedia's longterm legitimacy. Those engaging in ideological hijackings have (very rightly) realized that if they can define what is written about a movement on Wikipedia, they can control what society thinks about it.
Woo! What a line to start on. I had a kneejerk 'heck no' response, but I buy the author's argument that the verifiability criteria and upholding the prohibition against original research can negate most of the downsides of removing notability.
I worry that it could make Wikipedia harder to search, and that pages will need to be better indexed.
What if my name is Paul Ryan, and I create a Wikipedia page for all 798 other people named Paul Ryan (http://howmanyofme.com/people/Paul_Ryan/) using whitepages.com to satisfy verifiability so that when people try and find my Wikipedia page they are greeted by a disambiguation page that would be 12 printed pages long?
In order to prevent people from using the end of notability to obfuscate, I think that Wikipedia may need to switch to a more Google-like ranked search engine.
I think the argument is probably:
0.) some people have been historically advantaged over each other for non-meritocratic reasons.
1.) one of the ways people have been advantaged is itself in the notability of their actions.
[0]: http://listverse.com/2013/10/14/10-groundbreaking-women-scie...
[1]: http://io9.gizmodo.com/5077952/women-who-pretended-to-be-men...
[2]: https://www.wsj.com/articles/SB10001424127887324355904578159...
[3]: https://fivethirtyeight.com/datalab/are-female-scientists-hi...
2.) Therefore, using notability as a prerequisite for inclusion perpetuates a non-meritocratic historical bias.
To your question: "Is there any guarantee that getting rid of the notability criteria is going to result in a more meritocratic system?" I think that there are no guarantees in cultural changes, and the best way to be wrong about the outcomes of cultural change is to predict any outcome with certainty. That said, if uncertainty was a sufficient argument against cultural change, then we'd all be hunter/gatherers.