This is all your post looked like to me. Besides what people mentioned, another problem is that everything on laptops tends to be underclocked anyway or mobile versions. So incompatibilities and bottlenecks will also be in your way. There's a reason gaming laptops are expensive and putting a great card on a crappy system isn't the solution to your problem. :P

ExpressCard, though, is connected directly through a PCI Express single-lane (1x) bus - which, is likely not enough for powerful graphics (I think there are graphics cards for PCI Express 4-lane (4x) bus, but most are 16-lane as far as I'm aware).

They do already exist and also a box that you plug into a wall socket is called a desktop PC.

This. The suggestions about a separate box to hold a video card are a bit daft really. The principal benefit of a laptop is portability, if you then have to lug a box about the size of a mini PC around you lose that benefit. If you just have to play whilst not in front of a computer, pay the extra and get a gaming laptop. Personally I love my new work laptop, dell ultra book, its very light, long battery, and reasonable for most tasks, but if I want to play anything I would go upstairs and turn on the console or PC>

It exists. But it seems you'll need a Thunderbolt 3 port which only a few laptops have been released with so far.
http://www.gaminglaptopsjunky.com/external-gpu-with-thunderbolt-3usb-type-c/

Yes, ExpressCard is way better than USB3, but it still bottlenecks the graphics card. It is possible to use it for external graphics though and it at least seems to be somewhat useable.

Probably some good technical suggestions why it isn't done (or popular).

And here i thought it would be a large brick like the power supply for the 360 that would be your external video card being plugged in would be so ugly and useless for mobile uses. At which point you have to wonder why you aren't using a desktop...

But to be honest mobile hardware (ARM and low power chips) have come a very long way. Most likely if i get another high end video card, it will be on mobile architecture to have lower heating and power requirements.

Of course, there is a use for a dock-like solution as well in that you can just grab the machine and go off to wherever you're going without having to make sure the documents you need are available on the laptop when you leave the desktop but can also plug the laptop in to your extras and get more power when you're at your desk.

thunderbolt is the only viable way, i'm pretty sure we'll start seeing these products more often