Should the use of violence be institutionalized? Should one institution (or a set of institutions with a well-defined mode of cooperation) have a monopoly on violence? Can we have a stateless society in Max Weber's sense of "the state"?
There are, of course, alternative conceptions of "the state". Lenin offers an important conception: the state is the instrument of oppression and exploitation of one class against the rest of society. I suspect that Lenin's conception is definitional: an organization that has a monopoly on the legitimate use of violence that one class does not use to oppress and exploit the rest of society would not be a state in Lenin's sense. Lenin's point in The State and Revolution is, I think, more subtle: the capitalist ruling class has constructed the specific nature of the institutions of governance (i.e. Weber's state) to oppress and exploit the working class; therefore, if well-meaning communists simply occupy those institutions, they cannot create fundamental change. The very nature of the roles and institutional structure ineluctably force office-holders into a capitalist mode of the exercise of violence. Hence Lenin draws the distinctions between socialists and communists: Socialists believe — mistakenly, in Lenin's opinion — that the institutions of governance are, by and large, socially neutral, and we can achieve a socialist society simply by installing socialist individuals in these institutions. Communists, on the other hand, believe we must radically transform the fundamental institutions of governance to have a socialist (in the transitional sense) society.
Similarly, we can also talk about the trustee state vs the delegate state. In the trustee state, individuals who are members of the institutional state have personal power by virtue of their membership; this power is procedurally independent of the will and desire of the rest of the population. It is coherent, for example, for the trustee state to pass an unpopular law. In a delegate state, however, the members of the institutional state merely apply violence in accordance with the wishes of the population; it would be incoherent for a delegate state to pass an unpopular law. A delegate state would still fit Weber's definition, because only the institutional state would actually apply violence.
It seems easy to conflate "state" with "trustee state" because all states in the modern world are trustee states. It's also arguable that even if only the application of violence were delegated to a specific institution, the institution would quickly adopt a sense of privilege to determine when violence ought to be applied; they would consider themselves not delegates but trustees.
If we equate "state" with "trustee state", and call the delegate model something else, then yes, I'm all for abolishing "the state" immediately, and replacing it with a delegate model. If we mean abolishing the institutionalizing the application of violence, I'm much more skeptical. Such abolition might seem desirable, but I suspect it's not presently feasible.