ReynardFox: The real question is 'who would it be for?' The answer is only a small, niche audience that wouldn't be enough to support a console post-launch, something that absolutely needs mainstream reach and appeal to even have a chance at success.
PCs can use controllers as easily as consoles nowadays, so there's no real place for a GOG console outside of a handful of hardcore collectors, what unique selling point would it have? Classic PC games? How many of those even support or would work on a controller? Who's going to do the work to implement controls for games that don't have native controller support?
Then there's the hardware, how powerful would it be? How powerful could it be whilst not selling for a loss? What percentage of the GOG library, realistically, would be compatible? Just how many would want one over say, Steam Deck?
GOG also doesn't have the brand recognition to get by on, or influence many through sheer clout, if they did they'd have a lot more games than they do.
Really, there are a myriad of ways that a GOG console could, and likely would, fail.
You misunderstand me, this is not about a controller at all, and as I stated it would be a hybrid PC/Console, and a controller should just be an option for those games that support it.
GOG already have a small market share compared to Steam and Epic etc, and at the end of the day it is all about your target audience. So sure, some wouldn't want to pay extra for a console, but with a console you get great benefits, and we all eventually upgrade our PCs, every few years, which are more expensive, and in many cases it is due to better game support. A decently done console would last many years, and maybe the possibility of some upgrading.
Many of your negatives can be dealt with by providing a better game experience, which is a quite an issue for many folk, because of the differences in PC hardware. If a game just works on the GOG console without the user having to tweak anything, that will be a great selling point way beyond any notion of just pleasing hardcore collectors.
GOG would also make sure all their games, or perhaps up to a certain era or requirement, work on the console.
In the end, like most things in life, you get what you pay for.