Too much to go into here, but let me refer you to Harold McGee's less well known book, The Curious Cook: More Kitchen Science and Lore, where he has an entire chapter devoted to this topic, complete with tables for a whole bunch of fruits.
Almost any normal sorbet recipe will contain a decent amount of sugar, and strawberries are no exception. I'd guess probably 1/2-2/3 cup per pound of strawberries. Use a substitute if you have an aversion - honey, agave, raw cane sugar, whatever you prefer. (Of course, anything liquid is going to contain some water, and cause a bit of ice, but it's still doable.) A sorbet without any extra sugar, even when frozen normally in an ice cream maker, is going to end up with a very icy texture, which will probably keep you from experiencing the flavor as much. The sugar helps soften it.
The other common way to soften a sorbet is alcohol. Rosé wine (thank you, David Lebovitz) works quite well in a strawberry sorbet. Vodka can be your go-to liquor for any impromptu sorbet with other fruits, since it'll add alcohol without any flavors that clash. Beyond that, either look for recipes, or look for mixed drinks containing the fruit you're using.
You might also be having problems simply because your strawberries aren't that great. Did you freeze them, or were they storebought? If you bought the strawberries yourself, you'd know they were decent before freezing, while not all storebought frozen fruit is as flavorful.
Finally, it's possible that your frozen strawberries collected some extra water in the form of frost, which then makes your sorbet icier. If there are obvious big chunks you could scrape them off.
Best Answer
There are a few things to consider here. Firstly, sugar dissolves in hot water better than in cold water. So, regardless of other considerations, it's worth making a simple syrup of the water and sugar.
What will change by heating is a few things. From a taste standpoint, depending on how you cook the fruit, the sorbet may taste "cooked". If that's the flavor you're looking for, cook away! However, "fresher" tasting sorbets are made by just pureeing (and straining). Cooking the fruit also stops oxidation (and discoloring) which happens with some fruits. On the other hand, the acidic lime juice will help prevent oxidation. Speaking of lime juice, if it's freshly-squeezed, a large component to its flavor are the volatile citrus oils. Cooking will likely cause these to evaporate, thereby losing some "citrusy" flavor (the acidity will remain, though).
From a texture standpoint it depends on a few things. Cooked fruit is usually softer; when pureed it will contribute towards a smoother texture. Additionally, many fruits contain pectin which is released when cooking. Pectin will contribute positively to the resulting texture of the sorbet. However, overcooking does degrade the pectin.
One way to get the best of both worlds is to gently poach the fruit in the simple syrup to soften it and release the pectin. (Alternatively, you can sous vide the fruit.) If you really want the "fresh" flavor (my preference) but want the benefit of pectin you can add a hydrocolloid thickener like xanthan gum or guar gum in a small amount (usually under 1% by weight).