I believe they're referencing this:

The U.S. Supreme Court ruled Monday that state prisoners have no constitutional right to present new evidence in federal court to support their claims that they were represented at trial and on appeal in state courts by unqualified or otherwise deficient lawyers. The vote was 6-to-3, along ideological lines.

. . .

On Monday Thomas wrote the majority decision hollowing out that 2012 ruling on behalf of the court's new six-justice conservative super majority.

He said that federal courts may not hear "new evidence" obtained after conviction to show how deficient the trial or appellate lawyer in state court was. To allow such evidence to be presented in federal court, he said, "encourages prisoners to sandbag state courts," depriving the states of "the finality that is essential to both the retributive and deterrent function of criminal law."

. . .

Writing for the three dissenters, Justice Sonia Sotomayor called the decision "perverse," and "illogical." The Sixth Amendment "guarantees criminal defendants the right to effective assistance of counsel at trial," she said. "Today, however, the court hamstrings the federal courts' authority to safeguard that right."

NPR Source

This is so from 2022.

yes more then once. Most recently the supreme court ruled you can't bring new evidence to an areal. Why? because it would undermine the state right to be sure of their decision. Also note that the most successful way to win an appeal on a criminal case was to bring new evidence that showed your defense did not do their job or the prosecution withheld evidence that showed your innocence.

It's called "finality".

The idea that it's more Important that the process is followed and then stops at some point than that justice is achieved.

Same reason they barred introduction of new evidence when appealing from state court to federal, giving potentially corrupt state courts full power to block exculpatory evidence to deny someone justice because the federal courts must uphold the verdict if the evidence which was accepted indicates guilt under the state law. Same thing if the prosecutor knows of evidence of innocence and withholds or, or if the evidence only turns up after the trial. You get only one chance and then you're screwed.

Shinn V Ramirez, 2022.

They were arguing ineffective counsel post conviction because evidence wasn't submitted that could have shown Ramirez was innocent. Lower courts agreed, citing previous SCOTUS rulings. SCOTUS decided federal courts must be bound by the original evidence only.

Money Quote -

Two of those costs are particularly relevant here. First, a federal order to retry or release a state prisoner overrides the State’s sovereign power to enforce “societal norms through criminal law.” Calderon v. Thompson, 523 U. S. 538, 556.

Second, federal intervention imposes significant costs on state criminal justice systems. See, e.g., Wainwright v. Sykes, 433 U. S. 72, 90. Pp. 6–8.

(Separated for clarity)

Personally I love how they say we need to respect a state's right to enforce social norms. With the death penalty. Because those are equivalent things. Betty doesn't like to mow her lawn. She likes to let her neighbor Lucy do it. Off to the chair for her! Okay jokes aside what they mean is their power to make laws, enforce laws, and have a court system.

And then it's too expensive? Really? I'm not going to be surprised when we end up with the purge only instead of being everywhere it's actually when the air raid siren goes off during yard time at the prison.

Especially if the American Barber Association has a rule that none of its members may participate in the haircut; and scissor manufacturers all refuse to sell to you. So you end up having it done by a random person who doesn't mind ignoring what every barber says, using a pair of rusty scissors the sherrif was able to find at a garage sale.

Is there some reasoning behind that? As far as I know, there are at least some gas chambers in the US. And even if Alabama happens not to have one, it doesn't seem too complicated to build one.

For a home kit, there's a lot less potential for abuse. You don't need hard drugs, or any abused drugs, it's just nitrogen. The person doesn't have any feeling of suffocating, they just go to sleep. Similar to why carbon monoxide poisoning is so dangerous.

Because ODing can be a rough way to die. With nitrogen hypoxia you just go to sleep and never wake up.

We could also just not kill people. Kinda seems to be at the root of this problem.

Yeah the mask and timing is what caused that one prisoner to be in so much suffering since he knew it was going to happen imminently so he held his breath.

If it were done gradually over a period of like 30 minutes, he likely wouldn't have noticed and just drifted into unconsciousness.