It exists because his predecessors created the base of the village and made it almost impossible for him to fuck up (he fucked up anyway)
Hiruzen led the village through three, possible 4 wars and 1 natural disaster. And it kept bouncing back stronger than before. No Hokage has done as much as him.
He let Orochimaru get away with experimenting on members of his own village including pregnant women, unborn children, and his ninja. Enma (his summon partner) told him not to do it and he STILL let him go. This WOULD NOT have been an issue with the first 2 Hokage
This is the most info we're given on who Orochimaru experimented on within Konoha and yes, it is a failing of Hiruzen's.. He should've fought and killed Orochimaru but couldn't get over his personal feelings at the time. Hashirama came from an era where most of his siblings died before he was ten, Hiruzen was born and raised in Konoha—so while a failing it is, comparing it to someone who was more accustom to family and close bonds dying is a little unfair.
This isn't even getting into how bad he fucked up with the Uchiha/Danzo stuff
The Uchiha fucked themselves. Plot a coup 7 years after war ends, the Kyuubi attacks and kills your Hokage and 4 years after you barely evade war with Kumogakure? What sensible person even negotiates with the Uchiha like Hiruzen did? They're a massive risk to the village—more than Orochimaru—and Danzo forced his hand on this because if you let the Uchiha Clan attempt their coup, Konoha is being invaded within the year.