I vote no for several reasons.
Most of this is in defense of my opinion and directed at Zeth_Durron's difficult-to-swallow "argument" to the validity of releasing Left 4 Dead 2 as a separate game.
The look, feel, action, environment, goals, etc. are exactly the same as the first game. There are some differences; none of which could individually require a separate game to implement.
The idea that bugs are a valid reason for making l4d2 a new and separate game is silly. The elimination of bugs is the main reason for patching any application. (Why should a poorly implemented DLC capability be corrected when one can disguise a potential expansion as a completely separate game?) If you'll recall, the single player campaign is called a campaign (ironic isn't it). Some RTS's come with many campaigns; others, a few; still others, only one. Quite a few games offer the ability to add campaigns, via 3rd party mods, expansions, etc.
You referenced the DLC for Fallout, some of which didn't even (technically) happen in the same world as the original campaign (simulations, spaceships, et al), but they were still DLC and built on the core mechanics of the original game.
L4D2 is NO different. The director 2.0 you tout is no different than another set of scripts run when a level is played through. This is not a difficult task for a game designer to implement. This level automatically runs this set of scripts, plot data, actors, weapons, models, etc., etc.. Unless the designers were complete retards, it is no problem at all to change (with the original tools, of course) what set of scripts and resources are used in any given level.
Now if there needed to be significant engine changes in order to facilitate the depth of new features they planned for the new campaign, then they could easily have versioned up to a 1.5 or something to communicate the significant differences between the feature-set of the original and the updated in preparation for an expansion DLC.
Sure there are new weapons, and melee. Arguably these should have been in the first already. Why not patch this into the 1.5 as a bonus of getting the expansion? then customers could use new weapons in the original campaign, melee, etc.
Sure there are new locations, new gameplay types. Level differences and scripts. Absolutely not a reason for a new game.
A new UI, on the other hand, is pretty much required if you're going to make a new game. Mainly to address complaints and prevent confusion among players about which game they might be playing. It, in-and-of-itself, is no reason at all to make a new game. UI's go through several revisions during testing anyway. An expansion could change the UI, if only to signify it's presence or address problems with a prior one.
For the most part, Left 4 Dead is exactly the same as Left 4 Dead 2, except for a few superfluous differences: characters, locations, and features available to the player. Any expansion, DLC could add those differences. The plot is the same: zombie apocalypse. The mechanics are the same: kill zombies, using weapons and teamwork to survive. The universe is identical, save for different locations in the same country. There are new features in l4d2; this does not a new game make. New characters and locations do not make a new game, either. A new chapter or campaign, perhaps.
I can see doing it on the basis of extreme quality differences such as: 3x spoken dialog; higher-res textures and models on everything; 4x as many polys everywhere; new, more realistic, natural environment algorithms all around; use anything in the environment as a weapon, even the enemy. I would consider at least 2 of any of those necessary to qualify for a new game, versus an medium-larger expansion. Realistically, L4D2 didn't come close on any of those points.
I hold fast to the idea that Valve released it as a separate game simply to make more money. DLC could probably fetch $30 tops from customers, while a new game would go for $50. Less work for them, for more money in return. Let's call it greed—or capitalism, if you prefer.