No, it's not true that Europe does not have the death penalty because its systems are more insulated from populist impulses than the U.S. government

Regarding the death penalty, already (more than) a decade ago (thanks to Jim Miller), Josh Marshall had this to say:

You seldom hear conservatives note, disapprovingly, that "America is the only industrialized country in the world that doesn't have X." It's not hard to figure out why, since X usually involves European (or Canadian or Japanese) big government.
But liberals sometimes imagine that America's peculiar lack of, say, nationalized health care, tough gun control, decent child care, widespread mass transport, or substantial arts funding is a sign of political underdevelopment. And so they bemoan America's uniqueness.

Particularly on the death penalty … The flood of capital punishment horror stories … has left anti-death-penalty liberals more convinced than ever that, on this issue at least, American political culture is inferior to its counterparts across the Atlantic.

If only it were that simple. It's true that all of America's G-7 partners, save Japan, have abolished capital punishment, but the reason isn't, as death-penalty opponents usually assume, that their populations eschew vengeance. In fact, opinion polls show that Europeans and Canadians crave executions almost as much as their American counterparts do. It's just that their politicians don't listen to them. In other words, if these countries' political cultures are morally superior to America's, it's because they're less democratic.

…Differences in the way survey questions are framed complicate direct comparisons with Europe. …you find very few European countries where the public clearly opposes it, and there are a number where support is very strong. … There is barely a country in Europe where the death penalty was abolished in response to public opinion rather than in spite of it.

…Differences between European parliamentary government and the American separation-of-powers system also play a role. Parliamentary government may provide voters with more ideological variety, but it is much more resistant to political upstarts, outsiders, and the single-issue politics on which the death penalty thrives. In parliamentary systems, people tend to vote for parties, not individuals; and party committees choose which candidates stand for election. As a result, parties are less influenced by the odd new impulses that now and again bubble up from the electorate.

…Basically, then, Europe doesn't have the death penalty because its political systems are less democratic, or at least more insulated from populist impulses, than the U.S. government. And elites know it. Referring to France, a recent article in the UNESCO Courier noted that "action by courageous political leaders has been needed to overcome local public opinion that has remained mostly in favour of the death penalty."

…all over the industrialized world, it turns out that the men and women on the street like the death penalty. It's just that in Europe and Canada elites have exercised a kind of noblesse oblige. They've chosen a[n allegedly — ES] more civilized and humane political order over a fully popular and participatory one.