That gives you something far beyond formal legitimacy, which you already had.

Maximian tolerated Carausius' rule in Britain and on the continent but refused to grant the secessionist state formal legitimacy.

It followed a state-sponsored referendum this spring that lent formal legitimacy to a new constitution, though the new laws keep the republic squarely under Moscow's control.

Probably as part of seeking formal legitimacy, the break-away Gallic Empire had its own pairs of consuls during its existence (260-274).

Power can come from force, but formal legitimacy is often established, even if only by fictitious claims of continuity (e.g., a forged claim of descent from a previous dynasty).