In the US you have a right to appeal your sentence, which is a good thing. If the government is going to be killing people, we want to (at the very least) make sure they have dotted every “i” and crossed every “t”. You have to pay someone to read these appeals, typically an attorney or multiple attorneys and/or a judge. There can be a backlog so it can take awhile to get through all of them.
This is inherent to how capital punishment works in the US, and anything less would be borderline tyranny, so I reject your framing of it as “aberration or some dumb policy”.