Why did Hassan not fight for his caliphate?
Hassan(a.s)was already a caliphate of Allah but did not rule. Similarly, Prophet Ibraheem (a.s)Ismael, and Isaac were caliphates of Allah but did not rule.
Allah SWT says:
Or do they envy mankind for what Allah hath given them of his bounty? but We had already given the people of Abraham the Book and Wisdom and conferred upon them a great kingdom. Nisa:54 Does that make Ibraheem (a.s) not a caliphate if he did not have a kingdom? When did he rule in the first place? If he wasn’t given Baya”allegiance”does it make him not a caliphate?
Abraheem(a.s) Ismael and Isaac were caliphates but did not rule. The kingdom that they possesed was the caliphate, a possesion that was given from Allah swt.