Why isn't longevity a factor after the minimum requirement?
Practical reasons.
If I'm picking players for an ATG XI based on their peak, what's to stop me from defining that one ball Sreesanth bowled to Kallis as his 'peak', and thus picking him purely on the basis of that, ignoring all else?
This 'peak' has to be suitable size to ensure that what occurred within it wasn't simply a fluke or a one off. Anyone can bowl a really good ball once. Many, many players can bowl really good spells (Devon Malcom) or play incredible innings (Marlon Samuels) without being able to do it consistently over a reasonable period of time. So clearly in order to understand who a great player is, in order to differentiate actual high level ability from a purple patch, you need a minimum criteria of some sort. A minimum number of matches/innings over which this 'greatness' has to be demonstrated.
And what this level is will be arbitrary. It's essentially drawing a line in the sand. But it is necessary I feel, if for nothing else but to dwindle the pool of eligible players down to a more manageable size.
And yea, once you have this defined minimum level, you don't need to factor longevity in anymore. All players who have made the cut have proved that their brilliance was sustainable to your satisfaction. So if you are picking an ATG squad to take on another ATG squad, you might simply want a peak that lasts the length of a 5 match test series. If you're picking an ATG Squad to go on a world tour and play every other nation's ATG XI, you might want sustained brilliance over 30-40 test matches. If you want an ATG XI to win you 1 test match against a Martians XI, then I can see the argument of picking the 11 best single-test performances of all time.
This, however, is quite different to defining the overall 'Greatness' of a player. When it comes to overall Greatness, I feel longevity can only add value to a player, and not hurt them - IE, a player who averaged 50 over 30 tests isn't superior to one who averaged 50 over his first 30, and then 20 over his next 30, thus ending with an overall average of 35. If anything, the latter is superior, as he accomplished the same things the first player did + has those extra 30 tests at the end to boot.