I really don't think moderates join the right because they are more attractive. They do it because the Left went extreamist. What was left of center 40 years ago, is now considered right winged. I don't get how becoming a Left wing extremist is any better than becoming a right wing extremist. Republican views haven't really changed much, but Liberal veiws have changed pretty drastically in the last 50 years. This constant change alienates people. Its generally why as people age, they become more conservative.
I can definitely understand why it would feel that way but I do disagree. What looks like a shift to the left to some is just history doing its work its work to others. Things have simply accelerated due to literacy, a faster exchange of views and information, etc. Take your sentence about what Was leftwing 40 years ago now being considered rightwing. Just as a thought experiment, make that 100 and say it again - it would still be sort of true, even more so than 40. Letting women vote? Leftwing, not letting children work in factories? Leftwing! Allow interracial marriage? Leftwing! Now lets make that 50 years ago, just ten years before your point of reference for what is normal: it is now 1970, just a year after the Stonewall riots, it's another 8 years (two before your normal!) until Harvey Milk gets assasinated and right now homosexuality is illegal in almost all of the United States. Martin Luther King was assasinated just two years ago and the Montgomery march was just five years ago. The Civil Rights Act was passed two years ago before a background of massive riots in the streets. In Louisiana a law making the husband the sole owner of a couple's property wasn't overturned until 1981 - even after your normal! Marital rape wasn't illegal in all states until 1993 and its criminalization only started in the 70 s, so not being allowed to force yourself on your wife? Definitely leftwing!
Labor rights have continuously improved until the 1980s when they started being rolled back to the point where (I am admitedly quoting Wikipedia here) "In 2014, the United States received a poor grade of "4" on the ITUC's Global Rights Index, which ranks the worst places in the world for workers' rights, with "1" being the best and "5" the worst.[139] Other nations and regions that scored a "4" include Argentina, Bahrain, El Salvador, Haiti, Hong Kong, Iraq, Iran, Mexico and Yemen."
So there might be two lessons here: 1. Change and progress are normal and overall a good thing and 2. the main mistake of the American left probably was allowing the right to roll back labor rights and widen the income divide while playing poor white people against poor black people.