I'm curious to know what High Summoner problem? Is it the fact that there are only about 4 out of the entire millennium, indicating that Sin has only been killed 4 times (excluding Yunalesca), which implies that Sin should have killed everyone in spira by now?

If so, then this theory is quite similar to one of mine. With crusaders, warrior monks, boats and summoners all providng distractions for Sin, it is unlikely that Sin would have been killing all the time... Also, summoners may have been able to obtain the FA and battle Sin, but screw up because their bond with the aeon is not strong enough, thus having a final battle that may heavily damage Sin, but not fataly and causing it to go off for a few days to recover... That bit is part of my own theory...