but surely rejumpering when the duct for cabinet 7 runs past the front of the house would be in the hundreds, not thousands
I don't think you appreciate how the BT network is set up.
There is one or more big (up to 2000 pr) cables coming out of the exchange. Pairs are split out from this at various points, usually into smaller cables, and these end up at cabinets. These are known a E(xchange) side cables.
From each house in a specific area there is, either via an overhead or underground cable, a connection to a smaller cable. This is in turn connected, with others, to a slightly larger cable, and so on, until it gets back to a cabinet. These are known a D(istribution) side cables.
The cabinet is a cross connection point, that is its sole purpose, so a pair coming from the customer can, flexibly, be connected to a pair going back to the exchange.
So, to get from your house to a different cab, another cable would have to be run to link in to the other cabs distribution side. This is where it gets expensive.
Think of it as a mountain ridge with river valleys coming off it at intervals. All the valleys connect back to a big river at the bottom, but each has its own catchment area. Getting water from one valley to another would not be easy.