I think people have to look at the big picture here with regards to what we allow our own governments to do. You have to understand that individuals within every government always want to take a few extra inches and as such giving them any sort of power that may resemble a facist state can lead to a loss of balance and eventual loss of individual liberties. Always remember that all parts of society function like a bell curve.
Take for example intelligence - which is determined based on average IQ being 100 and a standard deviation being 15. If everyone's IQ suddenly doubled, or was halved, we'd still have the same measuring stick, simply "average" would mean something different. Crime, mental health, aptitude, physical ability, are all measured competitively. Even the concept of poverty isn't grounded in some moralistic anchor - people's standard of living today, which could be considered "poverty" might be far superior to the average standard of 100 years ago, or in a poorer country.
Therefore frusterations about people who of the herd who are "dragging ass" is pointless. If those people improved, the standards of "pulling your own weight" would go up and the same or others would then be considered the "ass draggers." For this reason, giving the government the power to try and cull the herd can be a scary proposition. Giving a legal distinction between contributing members of society is vastly troublesome as what we'd really be doing, when we talk about evolution enforced within a society, is eugenics.
What you're talking about, with execution as a "cost saving measure" is a streamlined process of this. Besides the obvious legal bias against minorities in criminal trials, as well as underprivileged, who may be for obvious reasons more likely to commit said crimes, are also far more likely to be wrongfully convicted, you have the potential jump in false positives, with innocent people wrongfully convicted as you weaken the appeals process to make executions more cost effective than imprisonment.
So now we're doing what? Executing the mentally imbalanced and the otherwise incapable of working? Not for that alone but that coupled with them committing crimes. You can't imprison them and keep them alive without paying the high cost, but at the same time you can't let them roam free as they pose a danger to society.
Let me offer a counter proposal, that I feel might be a more humane and practical solution:
First off while I'm not opposed to execution in theory, at the moment I think it's such an epic failure that it's rather pointless. Modern governments are too much of layered, inefficient beaurocracies to be given such awesome power as of now. Executions, as stated, in our current legal state(which is where we are, NOT fantasy land where murder trials are simple legal procedures), are too expensive and ultimately ineffective deterrents. Deterrents are based on a short time lapse between an action and a reaction. If people are executed for crimes they committed over a decade ago, it has served no practical purpose.
Next up, drug crimes. The prisons are full of dealers and users of illegal drugs. The reason for this? The drugs being illegal. If they were legal, and taxed, in the first place, it would speed up the clogged legal system, add tax revenue, and clear out prisons.
With the court system being sped up, punishments would be more effective as deterrents. Prison systems can also be easily curved cost wise without the need to brutalize criminals. I'm not going to go into details but prisons have a pretty wild range of cost/prisoners based on the management.
The truth of the matter, the higher the cost/prisoner ratio, the greater the higher the crime rate in the area. It's not that the criminals go straight, but they tend to do crimes in areas with more expensive prisons, where there quality of life inside will be better. If EVERY prison worked the same way, it's not known if crime rates themselves would just uniformly drop, but at any rate, it would lower costs.
Another thing to concern over - ex cons have a terrible time finding work. When you can't find a legitamate job, it's likely to fall back to crime as a way to make a living. I'd say try to educate criminals while they're in the system as a method to keep them away from crime, but most of you would probably respond that it would be rewarding them for committing crime(which wouldn't be wrong but it might be irrelevant).