This is the first box to do this in the UK, at least on the high street, but I recall there was a Japanese one that did the same thing, across all muxes, and possibly a BBC R&D project.
On the face of it, it's a neat idea - but to cover everything, you'd need seven tuners now, in areas where the temporary HD mux is available. And what happens if another mux is launched? You'd have a subset of channels that can't be recorded, which would confuse users.
The EE box manages 24 hours, across a selection of channels. If you were to do it for every channel, on every mux, for even 7 days, you'd need a lot more storage. To get up to the 30 days now offered by iPlayer, you'd need even more, and the cost of the boxes would likely go up a fair bit.
At some point, you're throwing quite a lot of extra money at each receiver, compared to the cost of a dumber one with no local storage. If that money were spent instead on upgrading the UK's broadband, it might make quite a difference. Plucking a figure from the air, you might well have the equivalent of over £100 per subscriber to spend on infrastructure.
Of course, the problem there is that the people saving the money (the broadband providers) aren't necessarily the ones who need to invest in the infrastructure, because the crucial parts of that are owned by BT Openreach. Because competition. Yay!
Nevertheless, it's a reasonable point - and perhaps hybrid systems where, for example, a few days catch up is stored locally on a disk and anything further back comes from the net, may well hit a sweet spot. It would be interesting to know the metrics, for instance, of how long after broadcast most programmes peak on services like iPlayer. Shifting some of that burden to the local device could be a stop-gap pending probably infrastructure upgrades.