I'm only using those as examples. Fallout 3 is wildly unspecific about what exactly is beyond the Capital Wasteland but presumably human civilization doesn't just disappear the second you leave the Capital Wasteland. Eden's solution in Fallout 3 is no solution at all because it doesn't address the issues of the wasteland beyond the tiny little section that is D.C. All the problems of the wasteland still exist just outside the borders and are going to keep spilling over into the Enclave's pacified area.
No mutated creatures would have been able to survive within the area and neither would any non-Enclave humans. The wasteland couldn't have just "reclaimed" the DC area, as stated in the Fallout 3 ending slides, the wasteland became a "graveyard" and the Enclave were allowed to grow and prosper there.
Yet even if the NCR collapses the societies that come after it will inevitably grow and seek to expand and they will do so with resources and a population base the Enclave can only dream of. It's research capabilities aren't significant enough to overcome the other incredible weaknesses they possess anymore than they were back in the time of Fallout 2. No matter how advanced the Enclave's technology is going to get, the West will be advancing as well. Just as all the APA in the world didn't enable the Enclave to take on the NCR in a straight up fight in Fallout 2, whatever technological edge the Enclave can amass is never going to be sufficient for them to cancel out the millions of men and vast amounts of resources and territory the societies in the West (and hell eventually Midwest, South, New England you name it) will possess.
Which is where an air-borne virus comes in.
They have to resort to the airborne solution eventually yet Eden's plan gets them no closer to achieving that goal and in many ways actively harms it by exposing themselves too soon in pursuit of a ridiculous objective (control of Project Purity).
The purifier is the key to cleansing the wasteland of mutations, including wiping out the Brotherhood of Steel and any other hostile forces. Prehaps an airborne version of the virus wasn't ready yet and would still take several years but the water-borne version was ready on the spot and could be deployed easily to wipe DC's slate clean so expansion could begin.
Again though just start with the airborne virus. Find another viable location to release it into the jetstream and set up new facilities there. Hell if you just want breathing room in D.C. for some reason don't worry about the damn jetstream just pump it into the air. It'll spread out and get as many mutants as the water version will. Eden is just fixated on Project Purity for no good reason.
We have to assume that an easier solution to DC-genocide was not yet available to the Enclave at the moment (and that the infected water solution was the easiest way), because I'm sure it would have been used. (also don't just assume that Raven Rock was not a viable location for the Jetstream, there may be other reasons that the airborne version was not released.)
I have to say now though, what you are close to arguing is that there is no real reason that the Enclave should have lost at DC (which I would agree with). With their technological capabilties and a genocide virus, they should have mopped the floor with the Brotherhood.
Besides what would the plot of Fallout 3 have been if there wasn't a fight over the purifier? Maybe there should have been a fight over an airborne virus releasing facility but then you have the plot of Fallout 2.
I have to agree with Okie here, so all of the water in the tidal basin and down river of DC is posioned? Eventualy word of mouth will spread and people will simply stop drinking the water or collect it for purification from the river north of the Purifier.
I guess they didn't though, or prehaps they didn't know it was the water, or prehaps there is an unknown factor that we don't quite understand (maybe when the water evaporates it produces a sort of local-airborne virus). The ending slides say, the DC area became a "graveyard".