What about putting a special SSD port on to the GPU like AMD already has done with some of its cards?
I agree that it would fix the issue but that brings another problem of what size SSD you use. You end up with two options
1. It is large enough to hold an enitre game, so 200+GB SSD on all GPUs that have onboard storage
Pros: Devs don't need to concern themselves with what is stored on the SSD they can simply request data like they would off the hard drive. So less programming work for devs.
Cons: Price. game loading speed? (since you would essentially need to copy the entire game file from one SSD to another)
2. Enough space to load either an entire linear level or a significant portion of an open world map. So 24GB-64GB
Pros: Cheaper
Cons: More work for devs as they will need to sort out what should go on the SSD. You also run into product segmentation issues if for example lower end card may only have 24GB but a top end card has 64GB. so they will need to work around that.
Load times would still be longer, due to copying so much data, just not as long as the above option.