It's not so daft really, but does need "considerable care" in implementation. Taking several things (some of them mentioned above, some not), in no particular order ...
1) In this case, "DP" means the distribution point close to the subscriber - the joint box up the pole or in the manhole close to your home. Not the Primary Distribution Point where the FTTC cabs are located.
2) There are already lots of situation where there is something using main power (utility power to our US cousins) between the exchange and the subscriber. Typically these devices run off a nominal 48V and have their own batteries. Maintenance of the batteries may be an issue - I decommissioned a rack (abandoned by it's telecoms company owner) of equipment at work a while ago, lets say the batteries in the bottom were "utterly and completely shagged".
3) Getting power from the cable in the street is technically very easy, but is also costly. There's a whole section in the FTTC cabinets for handling the power - input termination, isolation, overload protection, and only after all that does it get to the power supplies. Adding this lot to a FTTDP node would add considerably to both it's bulk and cost. There's also the cost of digging up the street and tapping into the power cable - this isn't a case of tipping a guy with a shovel a couple of tenners ! Interestingly, round my way I've observed FTTC cabinets where they've had to trench a lot further than I'd have expected to get to power.
4) Getting power from downstream isn't itself a daft idea. Most of us are already used to powering ethernet devices through the cabling, and we are pretty well all used to having our phones (a basic one at least) powered from the BT exchange. I see issues (as mentioned above) related to interaction and what if there aren't enough subscribers providing power in order to run the node.
For part of the node, there's not really much problem powering it off if that subscriber isn't powering it. But there will be a minimum core (upstream interface, management systems) that needs to be powered regardless of how many (or few) subscribers are powering it.
So there is a minimal power feed requirement, without which you can't run the node supervisory/control functions or communicate upstream.
5) Doing that powering safely is far from trivial. In theory each supply will have isolation at the supply end, but as this is all stuff under the subscribers' control then it cannot be assumed to be perfect. So the node must accept power from multiple lines, any of which could (through fault, incompetence, or malicious intent) be anything but a "safe" isolated extra-low voltage.
That aspect aside, a relatively simple switch mode PSU on each subscriber interface could provide isolation from the interface to the internal power supplies - while the internal management system takes care of only powering up the subscriber xDSL interface where there is a power feed present.
Some reasonable size capacitors could well be needed to handle some transient situations - two such situation that come to mind :
If there are two (worst case) powering subscribers and one stops providing power, then there will be a delay between loss of that subscriber's power and turning off the circuitry it power.
If all subscriber stop providing power (street wide power cut, or only one present and that gets disconnected) then ideally the node needs time to communicate upstream that's it's lost power and will be shutting down. Otherwise the management systems cannot differentiate between a node that's gone offline due to loss of power, or one that's lost it's connection (eg broken fibre) - and that's an important difference to know when it comes to fault management.
6) While it's still not FTTP, I can see why they'd want to do this. That last few yards from the bole/hole to the house is the most difficult and expensive bit. Often it's direct buried cable - so replacement mean digging up the road and subscribers drive or lawn.
Even where it's overhead, it's not automatically easy to replace - for example, a colleague had been told that his overhead cable doesn't meet current standards for height above the road. As long as it stays as it is then they can leave it, but the moment they do any work on it (such as replacing a failed cable) then they need to do it to current standards which means going to the chimney rather than soffit (it's a bungalow, and long span) with all the "work at height" issues that creates. Or they have to add another pole in the street to make a better span.