More than you'd think, given the metaphysically dead nature of the place; Poughkeepsie is not devoid of interest to a number of groups.
It should be noted that if the permanent angelic population around Poughkeepsie exceeds forty, it's not by much.
The Dreams of Poughkeepsie are drab things, to be sure: without a connection to the Marches they lose a certain savor. Blandine has set up a permanent research group to try and crack whatever it is that deadens the area. Said group alternates between stymieing Beleth's similar group, and simply ignoring them.
To be honest, most of the work that David could do there is already done by another Archangel; on the other hand, it is an ideal place for extreme sports enthusiasts. Then again, the definition of 'extreme sport' to a Servitor of Stone would encompass 'cleaning a neighborhood of its disruptive elements'; the lack of Essence and resonance just adds to the spice.
More than one fugitive from the Inquisition has gone to ground in Poughkeepsie - and the ones that do tend to be the ones with nothing to lose. Those charged with tracking down and bringing miscreants to Judgment will have to do so there without their esoteric abilities.
Guns still work, though.
Eli's Servitors discovered early on that their Archangel has a literal blind spot when it comes to Poughkeepsie. He cannot see it, doesn't remember anything about it, won't even recognize the name - it's as if the place wasn't there at all, which from the Symphony's hypothetical point of view is actually fairly accurate. Eli's Servitors did not react well to this bit of news, and are busily trying to figure out what the Hell is going on at that place.
In marked contrast to Eli (and to a lesser extent, everyone else), Gabriel has apparently not yet noticed that anything unusual is going on in Poughkeepsie. She routinely assigns angels there to punish particularly Cruel individuals... even though the Symphony is silent there. For that matter, she seems to have no troubles wandering the streets of the town. Madness mated with luck? Or does being the Word Made Fire allow her to transcend petty restrictions on her power? There are more than a few entities who would be interested in an answer.
Servitors of the Wind mostly react to Poughkeepsie in one of two ways: they either avoid it completely, or they hold races to see who can get closest to the edge at the highest speed without actually going over the line.
It is useful to have a place where prototypes may be tested without also having to screen for accidental and/or subconscious Essence expenditure. As for the anomaly itself: Jean has determined that the effects are not spreading, so the Servitors of Lightning on-site mostly perform routine data-gathering and what experiments that are not already being performed by Dreams and Creation.
Servitors of Animals are the backbone of the soul recovery teams; they can go places that humans cannot and Jordi is insistent that animal souls be brought out in an expedient matter. That this also means that more human souls are brought out from the Bubble is merely a side-effect; the Archangel of Animals doesn't much care one way or the other, but he knows that many of his colleagues do.
There are many locales in Poughkeepsie that make perfect places to discuss a plan without supernatural eavesdropping, store a metaphysically dangerous substance without fear of contamination or secure a mortal without needing esoteric cloaking mechanisms. The Commander of the Host anticipated the Archangel of War's observations along these lines by a good twelve hours - which pleased both of them, really.
Like Laurence, Marc finds advantages to having a place where deals may be made and planned without supernatural influence, of various sorts. He can also make the occasional deal with those also in the know... on both sides of the Bubble.
Laurence does the strategy, Michael does the tactics. Or more accurately, remedial training for those Servitors deemed likely to treat their celestial abilities as a crutch. A week or two in Poughkeepsie's discreet War-dojo will straighten that nonsense right out...
Like Blandine, Novalis works to cure the whatever-it-is that is causing the problem. She is also carefully encouraging the creation of a network of mortals to take up the slack. After all, just because the Symphony has forgotten Poughkeepsie doesn't mean that Heaven should.
Servitors of Destiny work with Animals to recover souls, and with Dreams and Flowers to determine the cause of the problem. It is rumored that Yves already knows the latter, but not in a manner that would allow him to reverse the effect - or that he could, but something else stays his hand. Either way, his angels continue to work on.
Saints and Soldiers
Both may operate inside the Bubble, although the former find it harder going than the latter. They prefer influence and infiltration over activism; their main purpose is to provide on-site analysis and observations in a relatively safe manner. They also act as the major mechanism by which people already Destined for Heaven are 'encouraged' not to permanently stay.