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If you're competitors really want to spy on you, they would spend the money for one month of your service so I would not worry about that.

Unless your potential customers are pre-sold on your software or they really need your software immediately, it will be difficult to convert them into paying customers. By having the free trial, it makes it easier to try it out without any monetary repercussions. Also, it's difficult to get approval at many companies to try a new software where they have to pay for it. Imagine your solution doesn't fit their needs. All of a sudden, the person that requested your software will look bad in front of colleagues and bosses. This is a very real risk people want to avoid at all cost.