Why an SSGN is a strike vessel rather than a complete cruiser

Is a guided-missile submarine effectively a cruiser?

Only in its covert strike function; it can deliver cruiser-like firepower but cannot perform the full visible and diplomatic cruiser role.

The SSGN functions first as a covert strike platform. Its missile load can reproduce the sudden offensive effect of a cruiser arriving, firing, and withdrawing. Stealth also makes the boat usable in situations where an irreplaceable visible surface ship might be held back. It still lacks the diplomatic, presence, and broader cruising functions that define a complete cruiser, so the analogy should not be stretched beyond the strike role.