Why shouldn't we simply keep our technology secret?

Sometimes that is the best option. Determining whether to go after a patent or to rely on trade secret protection is a very fact specific evaluation, but it can be the better way to go in some circumstances. One thing to be aware of is that if you do decide to keep the designs & code secret then you need to be prepared to really keep them secret. In order to maintain legal protection you need to make sure that you take reasonable steps to ensure the secrecy of the information. This can often be at odds with the need to advertise, get some publicity, and attract investors. Balancing the need to disclose with the need to keep things sufficiently secret can be tricky, but it can be a good option.