"TMKStB" == Too Many Kooks Spoil the Brothel writes:

TMKStB The collapse of matter towards the formation of a black hole
TMKStB should slow down indefinitely, observed "from outside", as it
TMKStB comes nearer and nearer to forming a horizon. Given the
TMKStB finite age of the Universe, I cannot see how any could by now
TMKStB have formed. ...

This is discussed at length in Misner, Thorne, & Wheeler. Briefly,
you are correct that it requires an infinite amount of time for an
external observer to see the surface of the star cross the horizon.
However, the light emitted from the surface of the star is also being
gravitationally redshifted. For a star of mass M, it takes roughly
only 10 microseconds*(M/M_sun) for the gravitational redshift to reach
a large value. As a result, the star essentially instantaneously
fades from view.

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