The overall total is fair, it's that you got 24 successes in a row (c 1 in 500) followed by 6 failures in a row (c 1/7000) so the chance of this happening (all the successes together and all the failures together) is less than one in a million.
The probability of that happening is the exact same as the probability of any other random sequence of hits and misses that average 80% and is well within the norm.
Long streaks that fall far outside the standard deviation are an aberration (and the odds of such an aberration occurring can be calculated), but that doesn't apply to your example.
What you're saying is the equivalent of saying that picking 1-2-3-4-5-6 as your lottery numbers is foolish because it has less of a chance of coming up due to being 'special'. In truth, that sequence has the same (infinitesimal) odds as any other combination of numbers, and is no less likely simply because the human brain sees a pattern in it.
As Arcana was saying earlier, the odds of a random number generator producing something that humans recognize as a pattern are surprisingly high due to how good we are at pattern recognition. Compare the example you gave to instead getting 6 failures in a row followed by 24 successes, or 12-6-12, or a failure every 6th time exactly (and there are at least 5 distinct sequences that do that with different phasing), and so on.
