That my friend is a very good question.
I agree, God wants us to have faith, but the fact is, and he knows this as well as we do, we don't always know if he will choose to intervene or not.
And since we don't know that, maybe we should be concerned, do the best we can to deal with something, then just trust him and "try" not to worry. Then hopefully, if we are living right, good will come of these things, or our prayers answered in the end, and we will realize there was nothing to worry about all along, then the next time we will worry a little less.
However it is absolutely true, no matter what, worry in itself will change nothing, and in certain cases it's nearly impossible not to. So maybe we can just get better at not worrying as we are given good reasons not to, as in what I mentioned.
The story of David and Goliath, they all worried, and God didn't hold it a against them, and still helped them out, so he does understand, for what that's worth.
I really wish I could do better than that, but I've given this a lot of thought over the last few yrs and that's the best I can do.