There is a practical, structural problem with the "war on terrorism" even as you've reframed it.
There's no way to eradicate "stateless radical Islamists", or even Al Qaeda (anyone can wave a black flag labeled "Al Qaeda"). So unlike a war on (say) Japan, the war on Al Qaeda can't end until a critical mass of politicians make the irrational decision to go on the record as saying we're finished prosecuting terrorists.
Historically, US foreign policy seems to get in the worst trouble when it declares itself a military adversary of concepts as opposed to states. See, for instance, "communism".
Strange that you picked that example, considering it's the only instance where you could hope to argue that the 'war' was successful. You don't see much Communism these days, at least not in the tradition of Stalin and Mao.
On the other hand drug use is still a worthy adversary despite the US having waged a long and bitter war of attrition against it for decades. Also poverty, obesity, probably a bunch of other pet struggles we appropriated the word 'war' for.
You're absolutely right that it's an open-ended commitment. And whether it's worth it--probably not to the degree we've spent money and lives on it, and distorted our internal politics in response to it. But I think the trends out there are deeply troubling. In 100 years, I want countries like the one my family is from to be like California, not Saudi Arabia. I think that would be good for them, but also good for us. But thanks to radical Islamists, the world is moving in the wrong direction. And if operations like ISIS can acquire and hold territory in countries that are theoretically friendly to the West, I think those are the kind of brush-fires that Western countries should undertake an open-ended commitment to putting out.