Our views depend on our priorities and the information we receive
Roberts is indeed a conservative. He doesn't bristle at the government's killing citizens (you know, the ones that can't vote anymore), but rather thinks it's bad policy, legal procedure-wise, to allow multiple appeals.
Apparently JR hasn't heard (that's the charitable interpretation, folks) of prosecutorial misconduct like the abuses at the Harris County (Houston) crime lab. "Losing" evidence and outright tampering of reports were only brought to light using multiple habeas corpus claims and direct appeals; that's what federal review of state murder trials is for. So Roberts' claim that the best way to keep from murdering innocent prisoners is to have the "best counsel available at every stage" rings hollow.
Here's a clue: the best counsel don't want to work for dirtbags. Oddly(?), there's more prestige (and of course, $) in helping a corporation pay less taxes than in trying to make sure the government's not framing poor people. Proponents of state murder love to trot out the "let them and their lawyers eat cake" argument in response to the fact that innocent people are killed, but given the economics of the situation it's just a smokescreen.
The fact that it takes numerous appeals, sometimes to the USSC from the TX CCA and the fed 5th C, sometimes twice because those courts won't listen the first time, shows that the system is stacked in such a way as to make this punishment cruel and unusual. Roberts should literally construct the 8th amendment, and if he needs help from international law to see that a culture of death and a beauracracy of murder, especially one so streamlined as that in Texas (which the fed system will soon resemble if Sen. Cornyn has his way of neutering habeas by imposing a three-prong set of hurdles to any HC claim), is brutal and fucked-up, then so be it.