Can I backfill without inspections using sight tubes?

I have not heard of such a thing that an inspector would allow a homeowner to use. As a professional I can drop a tape measure and take photos where safety is at risk with an open trench, depending on the size of the job only a minor inspection label may be required for a pro but never a homeowner in all of the states I have worked in the US. Are you in a location where you have heard of these “site tubes”?

I doubt the existence of any code requirement that an inspector must accept sight tubes. Even if there were, a local authority may simply say "nah, not gonna do it that way." Then what would, what could you do -- a fight over code is seldom truly won by the inspectee.

There are instances when it is literally impossible to visually check the depth of conduit: directional boring, for example. An inspector can see only the entrance and exit pits and has to trust the depth record made by the boring crew (if any was made at all). Other times an inspector may accept a photo of a measuring stick showing the depth. I'm not a full-time professional, but I've had an inspector accept both my directional bored work and my photos of an open trench. The biggest key is to earn their trust by being friendly, direct, and honest. Don't just barely meet code, either. In the case of a buried conduit go an inch or even two deeper than required unless there's a compelling reason not to -- in most conditions it isn't tremendously more work.

You can always try submitting a photo to the inspector. They'll probably respond in one of two ways: "thanks, carry on" or "schedule an appointment for me to see it in person."