Just the act of choosing an adventure to run is a function of your biases. Designing an adventure is an order of magnitude more dependent on one's biases. Every call you make during play is based on bias -- even if that bias is essentially "rules as written with no fudging die rolls."
As such, I don't think trying to be "unbiased" is a particularly useful goal. Exactly what a GM's job is varies from person to person, but I think most people would agree the primary function is to facilitate fun for everyone at the table (including themselves), whatever that means for the table in question. Embracing some biases and resisting others will be necessary to achieve that end.
This really strikes me as a reductio absurdum argument. If you think embracing some biases is fine, by all means, do so if it adds to your game. But I think telling people who try to be fair and impartial, and who find that adds to their game, that they never are because everything is bias, isn't particularly persuasive or helpful for either position in the discussion. Of course bias can enter in at any point, but you can also hold it in check. I think few people worry about it at the adventure design stage (though obviously fairness can be a consideration here too: for example is this challenge one where the players have a reasonable chance to discover they are being followed by a spy, etc). I think at any of those points, you can work to keep your biases in check. Again, just because you don't achieve 100% bias free in that moment, doesn't mean there is not a more biased way to handle it, and a less biased way to handle it. And I do think we would all agree fun is the end goal here, but what that means will vary. For a lot of us, an impartial ref is an important part of making the game more fun.