Along with everything else wrong with this: your icon is literally your brand, and you want your branding to be flawless + everywhere.
This would be like Nike putting an ugly pixelated version of their logo on cheaper sneakers to encourage you to buy more expensive ones; whatever pocket change they made from upgraders would be dwarfed by the damage it would do to their trademark.
The only thing I can come up with is when reddit was shitting the bed most egregiously, all of the news outlets were showing the app icon in images/thumbnails. Perhaps they wanted to distance a bit from the bad publicity?
Not that having a Doge button is any kind of brand recognition. I'd argue it's juvenile for such a "grown up company", or whatever Spez said about adult business, hehe.