The main reason the Supreme Court appears to have so much power is because our Legislative Branch has been slow to actually pass new laws, meaning the interpretation of existing laws to new scenarios is becoming more and more important.
Now, as a practical matter, the Supreme Court is a political creature and tends not to stray too far from popular opinion. Thus, the decision above was possible in 2015. It's likely not a right they'd have "discovered" in 1980.
However, the Supreme Court has certainly made decisions such as Brown v. Board of Education that were almost certainly not majority opinion even in many relatively liberal locations.
Now, as for the rest of your post - I completely agree.
Supreme Court's role is to be a stabilizing factor, because majority can switch from Democrats to Republicans every four years. Supreme Court's partisan composition is basically a moving average of the last 5-6 presidential election's results, thus smoothing out temporary whims of the society.
Two years, actually, assuming only regular elections and ignoring other changes in office-holding.