Why are broadcast checkpoints considered bad?
Centralized checkpoints is a mechanism whereby nodes trust a certain hardcoded key to make new checkpoints. This means that in case of a fork, the key owner can make the network choose any branch he wants, even the one which is shorter. If this key is compromised, an attacker can use it to mount an equivalent to 51% attack with any hash rate. This, together with that the developer should constantly do something (produce checkpoints) to keep the network secure, goes totally against the idea of decentralization. Without decentralization, a cryptocurrency has little advantage over traditional banking system.