Let's skip morality for a second.
First, US law - I tagged this question as USA because few other developed countries have this issue, besides Japan - forbids cruel and unusual punishment. So the execution needs to happen under as un-painful, un-stressful conditions as possible (if you think any execution is cruel ... that's not the point). This started being a problem when at least one person had to be repeatedly injected and showed signs of distress. Since the scrutiny started, this has been seen again on several occasions. So at least some of the current methods are open to legal criticism from the cruelty angle.
Second, the people doing the job may not be thrilled. From doctors and medical personnel (who may not be allowed to participate at all, see comments) to just people pulling triggers or power switches. So even something as "simple" as arranging someone who really knows how to administrate intravenous shots may be problematic if licensed medical personnel is not allowed to do it (and could lose their license in some circumstances). ref, ref, wiki re. participation medical personnel:
In 2010, the American Board of Anesthesiologists, a member board of the American Board of Medical Specialties, voted to revoke the certification of anesthesiologists who participate in executing a prisoner by lethal injection.
Third, the drug manufacturers sell very little volume of their products for this purpose but face massive PR backlash. Simplest solution is to just stop selling it for that purpose and expressly forbid their use for it. Very free market, hard to oppose from the PoV of someone opposing government overreach.
Fourth, regardless of whether it could legally be considered cruel and unusual, things that remind people too much of how barbaric capital executions are, are out: no guillotines, beheadings, etc... Optics are everything: you want something sterile, medical, scientific. Not something out of the Dark Ages or reminding too much of nasty regimes elsewhere. Wouldn't want to alienate your supporters. (note: it's not that guillotines are inhumane by the metrics of this subject - they're probably pretty darn good on speed, pain and ease of operation - they just look bad and remind death penalty supporters of exactly what they are supporting).
Fifth, opiates. Fentanyl is lethal, painless and presumably thoroughly enjoyable at the time. But the people most baying for the death penalty are also very opposed to recreational drugs. Probably sets off all sorts of cognitive dissonance. Plus, see comment below, they may not work that well either (I find this statement, all of 5 sec long, part of a comedy/news show very unconvincing about their effectiveness or not, at least with trained personnel. Links to better sources welcomed.). (as of 2019): Not used federally, on hold pending legal challenges in Nevada, used once in Nebraska, in combination:
There’s no particular reason why one would use fentanyl. No one has used it before, and we’ve had hundreds and hundreds of executions by injection. That suggests that the state is using fentanyl because it can get its hands on it.
- Robert Dunham, Death Penalty Information Center
Scott R. Frakes, the director of Nebraska’s Department of Correctional Services, admitted to this in an affidavit: “Lethal substances used in a lethal injection execution are difficult, if nearly impossible, to obtain.” Like the federal government, states are struggling to find companies that will sell them drugs for executions. In Ohio, the problem is so serious that lawmakers began debating last month whether their state should carry out executions with fentanyl confiscated from drug traffickers by the police.
Sixth the death penalty is not all that popular, not least because miscarriages of justice where innocent people are convicted have been known to happen (quite a bit), though not necessarily in capital punishment cases. So, to circle back to the question's core, there's a limited appetite for just "fixing the problem" and quite a bit of "arguing on technicalities".
"Requires no limited resources, guaranteed painless, looks inoffensive" - pick any 2 seems to be the dilemma. Although, to be honest, the electric chair, as answered here, competently-operated, might fit the bill.
p.s. The US death penalty is definitely a moving target. The US did not carry out any executions from 1966-1976, according to The Executioner's Song (book by N. Mailer). Then it came back, went up (peak 1999: 98), is now going down (2020: 17). Scrutiny about execution procedures is relatively new and is not far predated by systematic investigations of wrongful convictions in the US justice system. These are all items that have surfaced in the last 20 years or so. Pew Research makes some good reading, as usual.
Can you provide a reference for "Lethal injection however seems to be complicated by the procedure and substances...". I'm sure I remember hearing that a UK company was supplying all of one of the substances for lethal injection - and then stopped/refused. The US justice system struggled (and may still be struggling) to find anybody else who would. – Grimm The Opiner Feb 01 '23 at 13:48