You are not alone, even though you are mistaken. The concept of "A soft starter will save me a lot of money on startup costs" is a very common myth, often propagated by salesmen who are unable to articulate the REAL benefits of soft starters (as so eloquently laid out by Bob above). What's behind that myth is the misunderstood idea of savings on "Peak Demand Charges". People see a charge on their utility bill that reads something to that effect, so they think that if they lower the peak with a soft starter, the demand charge will go down. It just is not that simple. Peak demand charges are calculated based on what's called a "sliding window" of time, usually 15, 20 or 30 minutes. Any individual peak within that window is virtually ignored, other than the overall minuscule effect it has on the power consumption integrated over that time frame. So adding a soft starter has no tangible effect on changing the Demand Charge multiplier from your utility. If you call and ask them, they will explain it to you. Many people have been shocked to discover this after having spent the money on soft starters thinking that was the cure for their Peak Demand Charge ills.
What it DOES do is satisfy a SEPARATE requirement from the utility to limit your motor starting power, usually expressed as kVA/HP. The numbers vary from utility to utility so there is no universal number that will be the same across the country. But in GENERAL, it's usually somewhere around 50HP @ 480V (25HP @ 240V) and up requires SOME FORM of reduced voltage starting. A soft starter is one of the better ways to satisfy that, which adds the benefits Bob explained above. Those benefits all add up to money, but there is no advantage to leaving a motor running if it is not doing any useful work. No matter how you cut it, that is ZERO efficiency. When people have implemented soft starters on large machines and realized tangible energy savings, in my experiences they have always been the result of a behavior change that was barely noticed. Because of the myth of it costing too much to restart a machine, people would leave them running, just as you have. Then when they get the soft starter, they feel it is OK to shut them off when not used and restart them when needed. THAT saves the energy, but in reality it could also have saved the same amount without the soft starter had they turned it off. The soft starter just makes it "more OK" to do it without feeling like it's a problem. And in reality, they ARE preventing extra wear and tear on the machinery, so it a way, that is correct. It's just not really about the starting energy difference.