'This notion' is entirely in your own head, and your emotional response to what you thought I might have written is not making your case for rationality at all well.
I did not make a sentimental and emotional connection between the death penalty and civilisation. If you take the time to read what I actually wrote, you will see that it is revenge, not capital punishment, that I describe as 'the antithesis of civilisation'.
Civilisation is built upon the idea that victims have recourse to justice without the need for revenge, with its inevitable escalation into violent disorder and blood feuding.
Revenge is not a civilised reason to take any course of action - revenge is the epitome of uncivilised behaviour.
Given that my earlier argument ruled out other reasons for capital punishment, I conclude, without sentiment or emotion, that it is of no value to a civilised society.
Your reflexive dismissal of my argument as 'sentimental claptrap' might help you to imagine that your support for capital punishment is rational; but it is just a rationalisation - as is your assumption that the only reason to not share your viewpoint is squeamishness.
I am not particularly squeamish about killing. But there is no rational argument for capital punishment - the killing of a prisoner - that is compatible with civilisation; and I value civilisation far more than I value revenge.
There is one rational argument I would propose. For cases where the party is guilty beyond all reasonable doubt (murder in cold blood caught on clear video, for example), there is a cost savings to be had by executing the guilty party compared to the cost of putting them in prison for life (one estimate puts it at $31,286 per year average for the US, $168,000 for the city of New York:
source]
Let's use the average, surely a conservative estimate given that murderers often require a much higher security prison, and more effort/expense must be incurred to prevent their violent nature from being used against other inmates.
If someone is convicted of murder at age 30 (or younger), and they are expected to live until ~80 years, that is 50 years in prison at a total cost of $1,564,000.
This $1,564,000 could instead be spent to feed, house, and clothe innocent and non-violent people.
Compare this to the cost to save a life though the Against Malaria foundation
Cost per life saved
Using $5.30 as the total cost per net in Malawi and $7.50 for DRC, we estimate the cost per child life saved through an AMF-funded LLIN distribution at about $3,340.81
http://www.givewell.org/international/top-charities/amf#Costperlifesaved
So, the choice is, do we imprison a person guilty beyond all doubt of first-degree murder for $1,564,000+, or do we use that money to instead save ~470+ innocent lives (or some other more worthwhile use, whatever that may be)?