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In pure economic terms there is no rational argument for imprisoning people with no dependents for long periods of time; at some point it would be cheaper to execute (or exile - cf transportation) any convict, whatever crime they have committed and regardless of their mental state. Until the reforms of the 19th century it was indeed the position that a large range of what we would now regard as minor offences carried the death penalty.
However, there are a number of rational reasons why that may have undesirable consequences. In the first place, as the old saying goes, 'I may as well be hung for a sheep as a lamb' so there is an anti-deterrent effect. Second, there is a general feeling that justice requires that sentences should be proportionate to the offending - hence juries were often reluctant to convict where the death sentence would be the outcome and, for example, would find that the value of goods taken by a thief was less than a shilling in the teeth of evidence - which tended to bring the law into disrepute. There is little point in having a law which no-one is willing to obey. Further, where a prisoner who has previously been providing for his/her family cannot now do so, that family becomes a burden on the rest of us. Moreover, there is a considerable body of evidence which suggests that the children of such a family are statistically more likely to be less productive (more likely to have mental and general health problems, poorer educational outcomes and hence earn less, pay less in taxes and require more financial support) and thus cost more/contibute less. Where a death sentence is carried out, that prisoner can no longer prospectively be rehabilitated and turned into a useful and productive member of society so there may be an economic loss there too.
Of course there are other moral reasons why the death penalty should not be applied. One at least is the argument that we as a society should behave better than those who breach our basic standards.