I too do not doubt that if we had the death penalty, there would need to be a solid review/appeals procedure. But 10 years???? [*] Come on! You basically need at best a couple of teams of people to go through the evidence, talk to any witnesses etc., and figure out if there are any flaws in the evidence, and perhaps to go back to court to convince a team of judges either way. I can believe that, in a reasonable, efficient, system, that would take a few months - and that it might sometimes go on for longer if some reason turns up to doubt some of the evidence. But I cannot believe it has to take 10 years to do that. I'm going to hazard a guess that the reason it can take so long in the USA is that they have a very inefficient system, and lawyers and judges etc. go off to work on other cases for long periods in the meantime and so on.
I think that, if you really want to keep claiming that capital punishment would result in massive, long, cruel, delays like we see in America and would cost a fortune like we see in America, then you'd need to come up with some convincing argument to show that the American system probably is the best possible system for death penalty processes, and that it's close to being as efficient and quick and cost-effective as any reasonable system could ever be. Do you believe that is the case? I know I'm working on guesswork, without any detailed knowledge of the system, but I somehow doubt it is.
[*] I realize you said 'years', you yourself didn't specify '10' years, but you replied to someone who did suggest that timeframe without contradiction, so I'm assuming that's the kind of period you're implying appeals could take.