Before getting into the issues you raise, I think it's important to look at the broader context, which sees the convergence of two long-term historical trends and one more-recent one. To simplify, these are:
1. The collapse of a regional order in Islamic North and Sahelian Africa that dates back to the beginning of the post-colonial period. That order was based on support for repressive authoritarian regimes in return for stability. During the Cold War, stability was defined as anti-communist. In the late- and post-Cold War period, stability was defined as anti-Islamist (in the sense of political Islam). With the Arab Spring, and for other reasons in the Sahel, this exchange has become inacceptable. The new regional order is uncertain, unstable and has left everyone unprepared in terms of how to approach it strategically.
2. This collapse is taking place against the backdrop of an upsurge of fundamentalist Islam, with a small but very determined minority willing to use violence to achieve their vision of a "pure" Islamic state. This upsurge predated the collapse, but is now complicating it. Many of these movements are locally based with local objectives and varying degrees of religious extremism. (The Tuaregs in northern Mali, for instance, are divided between secular nationalists and Islamic jihadists.) However, there is again a small but motivated, highly mobile, well-financed and globalized cadre of jihadists able and willing to graft themselves onto regional movements that seem poised to achieve tactical success. This upsurge is just the latest iteration of a cyclical and at times violent ebb-and-flow tug-of-war between moderate Islam (usually trading cultures) and fundamentalist Islam that dates back to soon after Islam's spread to Northern and Sahelian Africa.
3. Both of these long-term trends are now converging with a more recent one, which can be thought of as a tactical/strategic stalemate between technologically advanced militaries (the U.S. and its European allies) and asymmetric local insurgencies and globalized terrorist networks. The initial military phase of the French intervention in Mali demonstrates that although insurgents armed with heavy arms and pick-up trucks can overwhelm the poorly trained and poorly equipped armies of their national governments, they do not stand a chance against a well-coordinated, combined arms campaign waged by even a small Western military contingent. But we also know from Afghanistan and Iraq that this is not enough to ensure "victory," defined as the achievement of our strategic objectives (a stable state, preferably democratic and aligned with the U.S., but at the least one that is compliant with global norms of state behavior). From there, many people make the mistake of concluding that the insurgents are destined to "win." This is misleading, though, because the conflicts of the past decade have demonstrated that neither side can achieve anything more than local tactical victories, defined as control of territory through presence, and wherever insurgents have achieved such local victories (the Pakistani tribal areas, areas of Yemen and Iraq), they have almost immediately turned the local population against them due to their implementation of a strict and brutal Islamic law that very few actually subscribe to. The result is that both sides are fighting a conflict that neither can win, in a strategic sense, without a willingness to commit endlessly to the application of violence.
Now we get to Obama, drones and the question of infinite war. For budgetary and political reasons, the U.S. can no longer commit to the kind of long-term state-building counterinsurgency campaigns we saw in Iraq and Afghanistan everywhere the threat of destabilization currently exists. It's important to add that, historically, these campaigns have been far from conclusively successful. Either way, until the advent of armed drone technology, abandoning boot-heavy counterinsurgency campaigns usually meant abandoning the fight altogether.
In this context, Obama's shift to drone and special operations strikes represents a trade-off: We know we can't win with boots on the ground, but at least this way, we will prevent the other side from winning, at a cost in money and (American) blood that we're willing to accept. The approach has long been known among the Israeli military (with regard to Hamas in Gaza) as "mowing the grass," and that term is now being used by the U.S. military as well. It acknowledges not only that such strikes will be inconclusive, but that it will be necessary to repeat them periodically.
You, like many critics of this approach, are now raising the moral cost it exacts. That is a valid and necessary effort, especially with regard to the lack of transparency and oversight in the process of target selection and the use of methods such as signature strikes, which, absent hard evidence of either the presence of a high-value individual target or knowledge of the location as a known gathering place of "bad guys," is arguably a war crime and perhaps a crime against humanity of the kind we are currently accusing Syrian President Bashar al-Assad of engaging in. Other critics question the tactical and especially the strategic effectiveness of drone strikes, while others worry about the precedent we are setting for other nations when they catch up to us in their drone capabilities. (Micah Zenko of the CFR is doing yeoman's work on this topic, by the way, in case you are not familiar with his work.)
I would just suggest that in weighing that balance, the choice is not between "infinite war" and "peace," but between "infinite war" and "persistent violence." Should the U.S. disengage from this fight, that violence will be directed by our current enemies toward the populations of the areas in question, but it will have indirect costs to regional stability, integration into global trade and supply chains (which, while not a panacea, do have an impact on local well-being), and humanitarian aid efforts. All of that is in addition to the potential threat of terrorist attacks against U.S. citizens and perhaps even the homeland. The final point I'd add is that the U.S. is the only nation on earth capable of conducting such a campaign, and if we do discontinue it, for all the valid and compelling reasons you and others have been developing, no one else will step in to contain these movements. That, too, needs to be considered.
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