The problem is he's asking for something that is literally impossible, AND he's asking for the wrong thing.
A VARIANCE is what you ask for if you are violating city by-laws or code. Say, your city requires that all houses be set back six feet from the curb. And your house is set back 5.5 feet from the curb. That's a situation to ask for a variance. In some cities, certain energy-conservation requirements can be exempted, usually for properties that have heritage value. Say, Mrs. Smith has beautiful stained glass windows, but they're not energy-efficient.
A variance cannot issue to evade a safety concern. There's even a recent, on topic case about what is required for a variance: Murphy v. LLC (Minn. Ct. App. 2025). This one affirmed the granting of a variance, but gave three steps that the court of appeal held are required to grant a variance. The third is that "If granted, the proposed variance will not be detrimental to the health, safety, or welfare of the general public or of those utilizing the property or nearby properties."
If the city mistakenly approves an unsafe, non-code improvement, and someone gets hurt, the city can be liable for it (Snyder v. City of Minneapolis).
An AFTER-THE-FACT PERMIT is what you look for if you (or the last guy who owned your house) have an improvement that required a permit but you (or the last guy) didn't get one. This requires you to file everything you needed for the original permit, AND pass an in-person, physical inspection. Remember (per Snyder), if the city doesn't inspect when it should have, the city can be liable for some dumbass getting hurt when it falls down.
He also has multiple problems with that guardrail: The gap between the railing and the wall looks more than 4", and I do not think they could support the required weight.