The gateway possibility is there, someone needs to do it, is all. There are instructions on the website on how to setup such a gateway on your local router, so you do not need to install the binary on each device to access ygg services.
The main reason why there isn't really anyone really doing this is that this is a research project and most people that use it, use it for their own usecases. Not to offer some websites which aren't already on mainnet.
On the other hand, you would have to run an Internet gateway on one of the nodes, and give that address as a default route. It would work, but with a bit more manual work. IIRC someone ran a public Internet gateway at some point.
The yggdrasil address-space is different from the one used to give public IPv6 addresses.