Consistency. It's easy to develop for a particular console because you know that they all have the same specs. Remove this, and developers have little reason to stay. Sure, you can upgrade your console to meet a certain performance of a game you want to play, but now developers have to develop for two different components. Considering that things like OpenGL matter incredibly as to what graphics card you are using (some graphics cards do not support the latest OpenGL) this means that developers now need to add new things to their OpenGL code specifically for the higher-end graphics cards, while also maintaining backwards compatibility. With the "vertical support" of the console being maintained indefinitely, this means that so must the code (newer GPUs, etc). Release-and-forget stops being a thing, and developers no longer have a reason to bother with consoles.
As someone who is developing with/familiar with console hardware and graphics in particular, it goes WAY beyond just this.
First and foremost: Console hardware is not general purpose PC hardware. It is custom designed, they often have hardware features which PCs or other consoles don't even have. We aren't talking just different GPU specs, we're talking 'oh hey, this device has a hardware unit built to compute this specific format of float point vectors.' For old game compatibility/emulation, some consoles have even had to physically build in redundant hardware from the previous generation because the hardware was just that unusual.
Second: these things are generally welded together, more or less. Putting together special slots so varying hardware from varying vendors works together adds physical size, expense, and usually some performance opportunity costs.
Third: Console hardware is custom built stuff. Microsoft, Sony, and so on, have their own hardware development teams that design and build these chips from the ground up. And not just build them. Because they are custom hardware, they need custom drivers. They usually have a custom OS too. Oh, and the aforementioned specialized hardware I mentioned? Yeah, you need APIs for that too. So you have special APIs akin to OpenGL which need to be written and designed from the ground up to maximize performance for applications on your platform. And usually, they have low-level graphics APIs similar to the proposed Vulkan spec.
In short, it's damn near impossible to get out a console with one set of hardware, let alone a bunch of redundant interchangeable crap to support.
Like, look at this silliness:
https://en.wikipedia.org/wiki/PlayStation_2_hardwareNot one, but 3 different pieces of hardware for processing floating point numbers; two of those being heterogeneous vector floating point units. Then a GPU on top of that. Also 2 Synergistic Processing Units, one of those from the PS1. Shit be complex.