The "advanced mode" rarely actually covers all the needs of an advanced user (because software is never quite everything to everyone), but it's at least better at handling both types of users.
Not all free software has this problem... Mozilla and Thunderbird I've had my parents on for years. It's not a ton to learn, and they work fine.
Taking the case of Photoshop vs. Gimp - I don't think the problem is complexity, lol. It's having to relearn everything once you're used to photoshop. (Conversely, I've never shelled out for Adobe products, and now don't want to have to relearn how to edit images in photoshop or illustrator)
Let's do another one. Windows Media Player (or more modern - "Movies & TV"). Users want to click on a video file and have it play with no fuss. VLC and MPC work fine for that! If you can manage to hold onto the file associations. That's why Microsoft tries so hard to grab and maintain the file associations.
I could go on... I think the thesis of this article is right for some pieces of software, but not all. It's worth considering - "all models are wrong, but some are useful".