Kevin I don't see any issue with the principle of generational curses because they clearly still exist one way or the other
When we go way back to the beginning when Adam and Eve sinned he brought the whole world into a generational curse and death was passed through that generational lineage, today science would call a lot of that type of thing genetic illnesses but this is all a result of the original curse of death and sickness and suffering being passed through that line I think the old covenant may have made that even stricter in a sense but revealed the truth of God's judgment that was passed down to sinful adamic creatures.
We see in the letter to the Roman church by the Apostle Paul we see Paul referring to this generational curse which came upon the whole gentle world although they knew god they didn't glorify God and give him honor and there foolish hearts became dark and professing to be wise they became fools and they changed the Glory of the incorruptible God into an image made like corruptible man and four footed animals and creeping things therefore God gave them over to a debase mind to do those things which are not fitting being filled with all unrighteousness and sexual immorality and wickedness and covered this full of envy murder and strife we see the world plagued by sickness demonic possession oppression.
The usage of the old covenant was to reveal it through the school master to Israel and to the world that those that come under the blood sacrifices prescribed by God would eventually be released from these generational curses and even get victory over the death sentence itself.
In theory you would expect that a person can be born again come under the new covenant partake in the sacrifice be filled baptised with the holy spirit and with fire and be set free from the generational curse but that doesn't seem to be the only way that God does things because he did also deliver people from demons as well which should have been dealt with through a simple new birth and baptism of the spirit.
If we can go into the early church exorcism and deliverance ministry renouncing the works of Satan were all part of breaking off that generational curse of death and sickness as a result of sin and coming into the blessing but then it's a matter of staying in that state and Christians do have a tendency to fall back into sin through the temptation of the devil so sometimes the demons have to be dealt with again other times there is never a thorough repentance and dealing with the generational curse.
When it Comes to a cultic witchcraft and curses this is the very nature of sorcery and why it was condemned by the God of the Bible because it was a dangerous demonic thing where the practitioner of sorcery can release a multitude of demons through the casting of spells into a family and those demons will continue to real havoc it in a family's life we see this in Africa and other places and until that witchcraft curse is broken the demons because of the power of sorcery will be able to torment the generations through that spell of witch craft.
The nature of witchcraft because it involves the sacrifice of animals and people and the blood being offered up to the demons and principalities it has extreme power over lives that are not sanctified and holy and are not covered with the blood of Christ efficiently and baptized and filled with the spirit as the seal.