Verifying Update Failure (iOS 10.3.3)

My iPhone 6 on iOS 10.2.1 hasn't been able to update over-the-air since 10.2.1. Every time, I download the new update, go to install it (OTA), and it hangs on Verifying Update, or eventually says "Unable to Install Update. An error has occurred installing iOS 10.3.3."

Does anyone know why this may happen? Is it a lack of needed free space? Does it have anything to do with 2-factor verification on our Apple account? Does it not work on wi-fi? Does it not normally work on LTE?

I've deleted the update multiple times and re downloaded, then tried to reinstall. I've made sure I have 4 GB of free space. I've disabled 2-factor verification on my account. And I've tried both wi-fi and through my cellular data.

The only thing I've ever found that addresses this problem is when people suggest to update via iTunes. This doesn't explain why these Verification Updates don't verify correctly, nor does this solve the problem for someone who uses an iDevice independently from iTunes.

iTunes is a solid work-around, but I'd love to know how to fix the problem so it will verify an OTA update instead of constantly being told to do it another way. If OTA updates are still something Apple supports, then they should have a fix/solution to the OTA updates not working, shouldn't they? And not just a work-around, suggesting to do it a different way, which requires the customer own another piece of computing hardware. Does anyone know how to fix a "Verifying Update" or "Unable to Install Update" failure?!? Or does everyone not know, including Apple's tech employees?!?