Also, your "your site" example is deceptively simple. It works nicely if your /48 happens to be full of 0s, but even assuming you were allocated a huge /32 and you got to choose the extra 16 bytes for memorability, the address is more likely to be something like 2a00:1450:4001:830::/48.
Even this seems overly optimistic. For example, www.google.com is not a /48, but seems to be closer to /124 from some basic probing: 2a00:1450:4001:830::2000 to 2a00:1450:4001:830::200f seem to all respond as www.google.com, but 2a00:1450:4001:830::2010 does not.
If Google chose not to allocate a whole /48 to www.google.com, I doubt many sites would.