It does. It also places the sender of that message on a level of societal advancement about on par with the 19th century.
Why not just go whole hog, and let's skip back to the beheadings and burning at the stake? Or drawing and quartering? Boiling alive? Flaying?
Why not? I don't see any reason you're giving that actually warrants
not doing any of that beyond the statement that it will make people think our society isn't "up to date".
If you argued that these methods are out of date because there are more humane methods of capital punishment and death penalty, then yes I agree. But not doing something (here I'm referring to anything, not specifically capital punishment) just because it's "old" and would make the society look "out of date" doesn't seem a valid reason all on its own to not do the "out of date" action.
Look at all the people with smart phones. Why use a flip phone? Don't use that, it's out of date and will make the society you live in look barbaric and not with the times.
Why have an economic system built around money? It's unfair and stops people from getting what they want because they don't have enough money, we'd look like barbarians to have poor and starving people in the current year when we had poor and starving people last year. Let's abolish the economy and have everyone take anything they want, that way we'll be progressive and not have starving or poor people like the society of yesteryear.
Why go to war with other countries? It's the current year, there were wars years ago. Surely society has advanced enough that we can settle our differences without violence and live in progressive harmony. Let's not look like barbarians.
etc.
I'll admit that I haven't been following this discussion and just kinda jumped in on a minor nitpick. I'm not arguing for or against public execution or in favor of certain methods of execution, just pointing out that "society looking out of date" seems an inadequate argument. It sounds very much like peer pressure ("look at all the other people smoking, you should smoke too! you don't want to look out of place, do you?" etc)