Well, first off, they will use more shadows, so your question is premature. Not quite sure if that should be in a spoiler tag or not. I assume this is a question regarding the TV-show, and not the books.
Secondly, the shadows are costly to summon. Later on in the books, it is mentioned that Stannis seems drained and skeletal, and there are also other references, which I will not post here for their very spolerific nature. But suffice to say, it concerns people getting hurt to fuel Melisandre's magic.
Also, as we shall see, the shadows will not help Stannis as much as he would hope, because the majority of the lords and people are against him. So, combined with their high cost, they do not provide a real answer to his problems.
Besides those reasons, I think Stannis is a good guy, deep down inside. At first, I did not like him at all, but throughout the books, he is solid, honourable, harsh and grumpy, and it is hard not to like him when he scorns and scolds his sycophants, but praises Davos for telling the truth.
All he does, he does for a reason, not for personal greed or ambition, but because it is right and just. Yes, I admit, I am a bit of a fan of Stannis. So, I am siding with Andres F and also saying that Stannis is not quite comfortable with it. He admits at one point that it is better to kill one man dishonourably, than to allow thousands to suffer, but I think it does not sit well with him just the same.