Popular election of judges isn't really a good way to bring Supreme Court decisions in line with public opinion. Elections just aren't about producing popular decisions. If you want popular decisions, you should just put the principles at stake up for a direct vote.
Look at the failure of universal background checks. We just saw an overwhelmingly popular measure fail to pass our elected Congress. There are a few reasons for that. One very important one is that the NRA, which is primarily a lobby for gun manufacturers, is willing to throw a lot of money at defeating politicians who are not sufficiently "pro-gun". Because background checks are so popular, the NRA wouldn't campaign against politicians by attacking them for voting for universal background checks. They would instead attack politicians on other issues - whatever's convenient. It doesn't matter to the NRA why people are voting against the politicians the NRA wants to punish. If judges have to campaign in the same way as Congressmen, expect the same sort of campaign finance issues.
There's also a strong culture war component. Background checks were something the Democrats wanted and were being pushed by Democratic politicians. Republican politicians may have been worried about losing support despite voting the same way their constituents would have, and despite their constituents knowing that, due to them being perceived as closer to the Democrats in general. The Court obviously already suffers from this to some extent, but making them into politicians would only make it worse.
The main advantage of appointed judges, to my mind, is that it increases the chances that judges are selected with an eye towards doing good in the long-run. Presidents are in a unique position in US politics in that they care a lot more about their legacies than anyone else. Congress is small-time enough that Congressmen are mostly just concerned with cozying up to business interests so as to achieve very comfortable retirements, but Presidents don't become lobbyists. Mostly they seem to jockey for position in the historical rankings. In office, they seem to try to move the country in the direction that they actually want it to go in (not the direction that they are paid to want it to go in, and especially in their second terms).
My feeling is that when the conservative justices win a decision, they're basically voting the way that Reagan or HW Bush or maybe W (if he cared enough) would have wanted them to vote independent of those presidents' political incentives. Likewise for the liberal justices and Clinton and Obama. You can probably tell more about Obama's political leanings from Kagan and Sotomayor's records than you can from his own time in office. The system basically works. It mostly fails because the Republican Party doesn't give a crap about anyone other than rich white men and these are lifetime appointments such that the appointment schedule is unpredictable and lumpy. If they had 18 year terms such that every presidential term saw two appointments, no single two-term president would be able to dominate the Court, it would only take 10 years for a determined population to give the Court a brand new majority, and we wouldn't have Scalia, Thomas, or Kennedy anymore.