The master-slave dialectic for Hegel is the driving force of history, its annulment is the end of history. The equalization of master-slave for Nietzsche brings with it a dissolving of their contradicting values (morality).
Is Nietzsche merely continuing the Hegelian necessity?
I think what Nietzsche foresaw that Hegel didn’t is that through destroying the dichotomies of master-slave; a transitionary period of nihilism would be initiated which leads into absolute spirit after its completion. Nihilism would create the fertile grounds for a revaluation of values, where the highest values devalue themselves and it is through this negation that new values can emerge. These values are part of an absolute morality (free from the contradictory values of master/slave) that is a constituent part of absolute spirit. I think Hegel was too preoccupied with the historical aspect of his system and Nietzsche picked it up on moral grounds where he expounded the moral implications of master/slave fading away.
This would be a Nietzschean objection: absolute morality is free from master/slave values but through creating new values it still perpetuates a moral system that is objective and not free for the individual; the difference of this morality compared with the old one is that it expels the dialectical opposition but still places objective moral principles that confine subjects in its morality.
I think that we have to accept, as social beings, the fundamental essence of morality is slavish; it unifies people and acts as an authority of value-positing for a ‘power’. It is a power structure you cannot rid a social group of because the social body is always comprised of power relations (a will to power); you can’t escape this element or else you go into moral-relativism which leads-again-into nihilism. The subjective morality Nietzsche advocates is a tumultuous transition of a process that gradually solidifies an objective morality. We can’t be morally subjective tenably; ‘will to power’ will always designate an object morality through a process of contradictions being resolved through time (subjective morality engenders the fecundity for antagonisms that reach a dialectical completion into a ‘universal’ morality). This newly completed morality will (possibly) never degrade into nihilism because it is not tensionally conflicting itself in a dialectic. I think Nietzsche’s greatest alluding task was creating the principles for which we could articulate and implement the process (unbeknownst to him) that fruitions this objective morality.
Nietzsche was a child of his times; a product of the historical milieu that manifested his individuality. He was a being in a specific point in history that found within his profound thought a kernel of an historical becoming. The thought he was trying to get away from (Hegelian Dialectics) was actually the very reality he was situated in. The events and philosophy that preceded him allowed him to elucidate what Hegel couldn’t: the coming of nihilism and the moralistic consequences that accompanied the end of the master/slave dialectic. Hegel had made the mistake of placing absolute spirit at the end of history; he could not foresee the moralistic implications and the turmoil that ‘the end’ would cause to ‘spirit’ from becoming absolute; spirit will have to go through an anguish of nihility, where it detaches itself from what constrained it, and then reconfigures itself in a process that will bring about its absolute completion. The thought of Nietzsche was able to continue Hegelian thought in a route that was not historically available for Hegel: this is why both thinkers should not be taken in conflicting terms; the alliance of their thought can be critically and genealogically used to unveil the hidden mechanisms of our society and reality.
Note: The Nietzschean “overman” is a bridge towards the Hegelian “absolute spirit”