It would appear from Perry's response that I haven't made myself quite clear on why permanent armed neutrality is not a viable foreign policy option of the US, in my view.
Let's try again, then, and look at it from a slightly different angle.
First, let's be clear about what neutrality is and what it is not. Neutrality is the (self)imposed obligation not to participate in an armed conflict between two subjects of international law. This is per se an ad hoc decision, so what Perry is looking for (and that's why I am insisting on it) is permanent neutrality. A state choosing permanent neutrality is additionally obliged to make sure that it is never in a situation where he is forced to take sides in an armed conflict. It is evident that being armed is useful in this regard.
Part of the confusion may be that we are not talking about the same thing, really. What Perry means by asking for US neutrality - if I may be so bold as to rephrase him - is not neutrality as defined above, but really a passive (a.k.a. isolationist) foreign policy.
So the question is: Why is an isolationist foreign policy bad for the US citizenry? Bad in Perry's view has two dimensions: economic welfare and (physical) security. On both accounts, the current policy is purportedly ineffective because a) growth would have been higher with "neutrality" (not substantiated), and b) Swiss nationals don't have to worry about being attacked for being Swiss.
Since Perry doesn't substantiate why an isolationist foreign policy would result in higher growth, I need not to into that (yet). As far as personal security of citizens abroad is concerned (that's the only aspect of security, apparently?) I think that isolationism doesn't reduce the threat to US citizens abroad. They are being targeted because of the US' size and importance and economic interests in the world, and those can be taken hostage regardless of the foreign policy stance. Switzerland is simply to irrelevant to provide terrorists leverage, and the US, try as it may, can never be as irrelevant.
Mind you, I am not advocating the current dilettantish foreign policy stance - my preference is with a multilateral, predictable foreign policy stance based on national interest and the rule of law.