I did have my deck permitted and inspected. It was a multi-stage process that required inspection in order to move forward. After digging the post holes, they came to inspect. I can’t remember if there was one more inspection or two, but it wasn’t a big deal – you just called the morning of the day you wanted an inspection, and they came and gave you a green card to move forward.
I can’t see the reason to get a permit, but not an inspection. Once you apply for the permit, they know you are building, and where, and one of their inspectors can stop by anyway. And the permit expires after a time, so I think that the DCRA database will show that you applied for a permit, but never received approval for the structure. I found the permitting process way more burdensome than the inspection process. Some people skip the entire process. You risk getting caught and given a stop work order and a fine, or could face issues once you want to sell. Not to mention that the whole process is for your own protection. I can see why people go for an all or nothing approach, but don’t really see an upside to your half-way option.