If you can get whatever superpowers you want by believing hard enough, then seeking external power is meaningless. An awful lot of stuff in D&D seems pretty pointless if that's true.
Your logic applies to theistic clerics, too. "If you can get magic from just worshipping a god, why would anyone go through the trouble of studying to become a Wizard or Bard? A lot of D&D classes seem pointless if a literal Deus Ex Machina can grant full spellcasting to anyone devoted to a god." The reason why both arguments are wrong is because there's more to being a Cleric besides having a favorite god or philosophy.
The answer to how Clerics channel divine power could be whatever you want it to be as a DM/world designer. Maybe the narcissistic cleric literally has to pray to themselves daily (like older editions had for theistic clerics), severely alter how they treat others because they think everyone is beneath them, or has to write scriptures based on self worship that they have to adhere too. Or they have to forfeit worldly possessions, restrict their diet, take a code of honor (for paladins), or any number of ways to restrict roleplay in a way that feels clerical.
Again, what I am talking about isn't simply "believing in yourself" or having self confidence. It would be channeling the power of belief/soul magic through similar means that theistic clerics do. This could appear in any manner of ways, whether it's a narcissistic egomania, a Buddhist/Mormon belief in self-perfection and enlightenment, or channeling the magic of your soul to produce miracles.
The folly in your viewpoint is that you stubbornly believe that it would be inherently easier to get cleric magic without a patron deity (or assuming that people who want to play clerics without a god want to do so as a short cut of getting power without actually working for it). The extremely simple and obvious solution to this is that you make it as difficult to gain magic as a nontheistic/narcissistic cleric/paladin as it is as a theistic cleric/paladin.
I enjoy and allow the concept of a nontheistic cleric because I like the themes you can explore with it. Tackling the Planescapian/Discworldian concept of belief as power. Allowing for Buddhist-inspired Clerics, whose power is channeled through drastically changing their lives in an effort to gain self-perfection. The nuanced and unanswered debate from Eberron about whether divine magic comes from divine beings (like the settings' inactive pantheon, the couatl magic of the Silver Flame, or extraplanar entities), your soul/divine spark (The Becoming God/Blood of Vol), or sheer belief in and devotion to the divine. The mutability of settings like Theros, where new religions can pop up by cult leaders gaining enough fanatical devotion from a religious/political following and how that can set up adventure hooks.
Edit: I like how open ended and inspiring the concept is. If you take a few minutes to think about the possibilities, it just allows for so many possible religions that restricting clerics to choosing a specific god to follow doesn't allow for. Not that the standard type of cleric is bad, I just prefer the Eberron approach. Others disagree, and that's okay too. I just think a lot of the proposed "issues" with the concept are leaping to conclusions that the premise doesn't lead to and I'm pushing back on the dismissive "OneTrueWay" attitude some people have.