Why is the Supreme Court not balanced in terms of their political views?
It is. The court is currently split with two reliable conservatives, two conservative-leaning swing votes, and four liberals. That's what you wanted, right? An even split between right wing and left wing?
It's worth noting that at one time (1995-2004), all but two justices on the Supreme Court were appointed by Republicans. Of those Republican appointees, four were considered swing voters at some level (John Paul Stevens, David Souter, Sandra Day O'Connor, and Anthony Kennedy). At the time of their retirements, Stevens and Souter were considered reliable liberal votes.
I'm not sure that you appreciate the difficulties that occur with tied decisions. They essentially leave the lower court rulings in place. This means not only that different parts of the country may effectively have different law (the lower courts are regional), but that the law may be determined by which court happens to hear the case first. While lower court rulings are not binding on other courts, they are still citable in other decisions in the absence of binding precedent.
Yes, you could make different tie resolution systems. The problem is that most of them are worse. For example, if the default is to favor the defending party, then you might see anti-abortion lawyers taking the pro-abortion side in a case hoping for a tie that would give the anti-abortion side the effective win. Pro-abortion lawyers would then try to maneuver so that their case taking the anti-abortion side as the plaintiff would come up first.
The situation is not as extreme as it may seem. Replacing Antonin Scalia with a more liberal candidate doesn't necessarily make that person determine the voting result. Instead, it shifts the median vote from Kennedy (or John Roberts) to Stephen Breyer. If Merrick Garland were confirmed, he might become the median vote. But that's because he is one of the more moderate potential justices.
It's also worth noting that while the most controversial decisions are often decided 5-4 with conservatives on one side and liberals on the other, that most decisions have different balances. A fair number of decisions are unanimous. Some decisions have alternate balances like the 5-4 decision in Cherokee Basin v. Owens that had Elena Kagan voting with Clarence Thomas and Samuel Alito voting with Sonia Sotomayor. Note that while Thomas and Sotomayor have the lowest likelihood of voting together in the current term, they still vote together 50% of the time.
And that obscures things somewhat. There are many areas on which the members of the Supreme Court are in agreement but on which they never rule. If there is no lower court disagreement, the Supreme Court can just leave the lower court rulings in place. So Supreme Court cases are already controversial and they still ended in unanimous decisions thirty out of seventy-four times in 2014. That's more than the nineteen decisions that ended 5-4.
And the truth is that until the 1980s, Republicans were as likely to appoint liberal justices as Democrats. Gerald Ford appointed Stevens. Richard Nixon appointed Harry Blackmun. John F. Kennedy appointed conservative Byron White. As late as 1990, George H. W. Bush appointed liberal Souter. Conservatives aren't exactly happy with the performance of George W. Bush appointee Roberts. Translate that to your evenly divided court and your 5-5 tie turns into a 6-4 left wing advantage.
If even the nominating presidents can't determine if the candidate is left or right wing, then how do you expect someone else to do so?