A point none of the other answers have addressed is that in a typical one party state, not many people are party members. In a typical case, 1%-5% of eligible voter are members of the sole recognized political party, which is along the same lines as the percentage of people in multi-party democracies who actively participate in person in the activities of a political party.
Entry into the sole, or dominant, political party is not open. One has to apply, be vetted for membership in a fairly involved review and background check by party officials, and be found worthy, to become a party member.
Once you are a party member, you have heightened levels of responsibility to toe the party line in public in order to continue to maintain your status as a loyal party member, and have a duty to do participate in your share of party activities and tasks, commensurate with your position within the party.
In exchange, party members, collectively, have a monopoly on political power, to the complete exclusion of non-members of the party. Party members also often get perks in other aspects of life, somewhat akin to the proverbial "old boy's network" or the nepotistic favors that people give their relatives in clan based societies.
From an institutional perspective, this is a way to keep lazy, stupid, and troublesome people out of the political process, allowing the party to maintain a united consensus in favor the policies it seeks to implement, and to arguably make better choices about which policies to favor than it might if all adults were meaningfully included in that process.
This can be particularly important in a state with many people who are ill informed or functionally illiterate, where there is not a historical tradition of democratic self-government by a mass franchise, and where the workings of government and the implications of different kinds of policies are not widely understood by the general population.
Put another way, while it is legitimate to worry about one faction having unfair control of the political process to the exclusion of other political factions, often, an equally pressing problem for a state is finding some way to develop enough of a consensus to build majority support in favor of conducting any activities of government at all to meet the people's needs in a halfway sensible manner. Typically, not long before the one party state was established, these issues were left in the hands of an externally imposed and controlled colonial regimes chosen through a nominally merit based civil service hiring process, or in the hands of a hereditary monarch with a supporting aristocracy that owes duties of loyalty to that monarch, all of whom were trained their entire lives to fill these roles that they knew they would have to fill someday.
For non-monarchies to function, every year, there needs to be majority support in favor of some leadership team with some budget to carry out some set of policies that meet the needs of the people of the state in a manner sufficiently to prevent the state from collapsing. In many newly self-governing non-monarchies, this bare minimum threshold is a non-trivial and daunting challenge, in and of itself, for anyone trying in good faith to achieve it, even in the absence of factious and time consuming infighting between numerous small interest groups within the society over the right course of action to take at a big picture level.
Also, with rare exceptions like North Korea, most one party states are not de facto monarchies. The party leadership is still selected on a non-hereditary basis within the party as vacancies emerge, typically with rank and file members electing delegates to the next level, for multiple levels of the party organization, until the process culminates in the party's central committee at the top. The upper levels of the party aren't necessarily entirely neutral and indifferent towards competing party members seeking to move up to the next level of the party organization in this process. But as a simple matter of logistical reality, the upper levels of the party don't have the capacity as a practical matter to determine precisely who ends up in intermediate level posts within the sole political party's organizational structure, like the local government central committee, or a regional government central committee, or subject matter committees tasked with dealing with some particular issue or specialized function of the party's responsibilities.
From the point of view of the people who establish the system in the first place, it insures that the legacy of their initial (usually revolutionary) agenda is carried on in continual succession by people who are more or less loyal to and believe in that agenda (or at least pretend to believe in it) long after they leave the political scene, while still implementing that agenda through groups of human beings who are living in whatever the current situation may be, affording the agenda a flexibility going forward that it might otherwise lack. Without the corps of carefully recruited party members needed to operationalize the party's vision, the party might be rendered too rigid to deal with changing circumstances over time.