The window of time when perfect total eclipse is possible:
Perfect total eclipse of the Sun by the Moon can only be witnessed from Earth within a 1% window of the estimated 10 billion-year life of the Sun and our solar system . . . . . . or 100,000,000 years.
From a Scientific American article entitled The Solar Eclipse Coincidence, by Caleb A. Scharf, May 18th, 2012:
‘It is an interesting coincidence that the Moon should so nearly perfectly blot out the Sun, since there is really no physical reason why this has been the case . . . Every year the Moon's orbit grows by some 3.8 centimeters and our day lengthens by about 0.000015 seconds. At this present rate, in about 50 million years the Moon will never completely eclipse the Sun, it will simply appear too small in the sky. This orbital evolution also implies that total solar eclipses in the distant past would have been just that - completely obliterating the Sun from view. It is very likely that a scientifically minded Tyrannosaurus Rex never got to see the circle of fire, or Baily's Beads in an eclipse and annular eclipses of the Sun.
So is there some great significance to the fact that we humans just happen to exist at a time when the Moon and Sun appear almost identically large in our skies? Nope, we're just landing in a window of opportunity that's probably about 100 million years wide, nothing obviously special, just rather good luck.'
'just rather good luck' . . . 'a happy coincidence'
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