Here is the URL pattern:
<width> and <height> seem to have no effect.
Example around the White House:
A tile is just on "view" of the underlying open data. It's really just an arbitrary computation based on osm data.
So, even if your "snapshot" of tiles would be only around 10GB or so, these tiles are often not just cached static images but rather have to be (pre)rendered anew, at least every once a time, because the underlying map data is changed. So: it's ...