In our experience, a trading strategy that is profitable from back-test does not guarantee the strategy will remain profitable in the future; but a strategy that is NOT profitable in back-test, has a very high chance of failing miserably in live trading.
So a carefully designed back-test would save the investor unnecessary time and money in trading the strategies that are not profitable in the past. And focus the time in allocating capital in the strategies that have performed well in back-test.
A good back-test analysis would improve the odds of having a robust and successful trading strategy in the long run.
It can help you build confidence on your own trading strategies and not to let your emotions affect your trading.