Setting aside for the moment the question of whether this would be theoretically desirable, I believe it is extremely unrealistic.
(1) Brad Spangler's suggestion of how to shut down the Libertarian Party involves amending the LP bylaws at a convention. But that must be done by LP members who actually take the trouble to become delegates and attend such a gathering. I highly doubt Spangler or similar-minded others will be able to mobilize any significant number of people to attend a party convention for the sole purpose of shutting down the organization. First they would face the daunting prospect of convincing people who are dead-set against the party to join it, then they would have to overcome any rule changes or counter-measures designed to repel their effort by those currently running the party.
(2) The Libertarian Party name is too well known and has too much market value to simply dry up and go away. Even if the present LP *were* to somehow go out of existence, someone would soon start another party with the same name. And even if people with the intent of keeping it off the market were able to wrest legal control of the party name, nationally and in all 50 states -- undoubtedly another huge struggle -- I very much doubt such a situation would last. Sooner or later the temptation to utilize such a politically valuable property to rebuild an LP along the lines of their own preferences, or to somehow turn a profit from it, rather than just sitting on it, would become too great for someone to resist.
(3) LP members are extremely unlikely to vote to disband the party at the behest of people who have long been critics of the party and have little credibility with those they'd need to convince, especially in the absence of a viable alternative. Vague references to working within the establishment parties or groups like ISIL and the Advocates for Self-Government do not constitute a plan, not even a bad one. LP members would reasonably ask themselves, why do we need to trash the LP in order to do these things? Many Libertarians already support or work within these other organizations, and except for the Ron Paul campaign (and at this point no longer even that, unless he switches gears and runs for president outside the GOP) do not appear any more than does the LP itself to be in a position such that a fresh infusion of activists, funds, etc., could conceivably result in a major breakthrough.
Spangler has a point that non-electoral strategies for long-term radical change have been to some degree neglected. But what are he or others doing about it? The LP need not preclude such strategies. There is no rule that says a political party must do X and only X, despite what some Libertarians seem to think. The LP is a strong potential vehicle for a mass movement that pursues non-electoral strategies along with electoral ones -- we just need the courage and imagination to think outside the box and recreate the party to match the opportunities and needs of the freedom movement, rather than assuming we must focus solely or primarily on elections because "that's what political parties do."
What's more, the Libertarian Party does not exist only in the United States. Nationalist-thinking United Statians tend to assume the libertarian movement revolves around the U.S. and will always do so. That may still be largely true at present, but if trends of globalization and faster-growing economies and populations elsewhere continue, there is no reason to expect it to be true in the future. There are already many Libertarian parties outside the U.S., as well as other libertarian organizations, and any well-formulated plan for the libertarian movement will take these into consideration. Aside from a reference to ISIL, (and one comment from a German source that appears supportive), Spangler's appeal appears not to consider the global picture.
My appeal to anarchists and others who think the libertarian movement would be better off without the Libertarian Party is this -- rather than waste your energy trying to tear down the party, build alternative institutions that could serve as effective vehicles for a mass movement, and attract Libertarian activists to them, as the Ron Paul campaign did, by showing us something that appears to have more energy and potential. Meanwhile, the Libertarian Party remains, imho, the best long-term/mass movement/radical vehicle that we have.
Love & Liberty,
((( starchild )))