How do you miss the monthly-odd posts of Yet Another Prisoner Jailed For 20 Years Found Innocent here on HN? Again and again and again it's shown that the justice system can get it wrong. The death penalty doesn't reduce the crime rate, it's not cheaper, it consumes more legal resources, and it's philosophically unsound. The only thing the death penalty does do is slake a thirst for vindictiveness.
If you're atheist, well, there's no 'heaven' to make it up to an actually-innocent convict (and their still-living loved ones). There is nothing you can do to 'make it better', not even in a token manner.
If you're a nihilist, well, it's the more expensive, labour-intensive path, requiring more effort. If nothing really matters, then why go to the extra effort?
And if you're proposing we treat humans the same way we treat dogs, then you should be aware that the number of dogs we kill for 'malfunctioning' (biting) is a rounding error of all the dogs we intentionally kill. If we were to treat humans like dogs, then for each of us there'd be someone deciding whether or not a person was convenient to have around (not necessarily someone that we even knew existed). Then we'd either be given a lethal injection if the decider was nice, or be killed in a variety of increasingly unpleasant ways if the decider wasn't. We kill an awful lot of canines (and all common pets) just because we can't be bothered to keep them around, from abandoned pets to puppy farms to feral culls to just getting rid of a pet's unwanted litter. Given all that, it seems odd to make much of a fuss over a 'broken' animal.
Final thought:
> but I don't believe execution is suffering
The act itself is largely not, but the lead-up to it is.