[DEV Question] Why is this allowed?

[Rongway]

If we could change weapon inside a duty while not switching class that would never happen.

You can.
The only place where your weapon is locked is the Hydra trial.

[ZioSerpe]

You can.
The only place where your weapon is locked is the Hydra trial.

You can at the end, during it wouldn't allow it, I remember once I did the exact opposite while doing WoD for light where I went in with legit weapon instead of relic, and I could not change during the run.

[Cylla]

You can at the end, during it wouldn't allow it, I remember once I did the exact opposite while doing WoD for light where I went in with legit weapon instead of relic, and I could not change during the run.

As long as nobody is fighting, you can change your weapon as you enter. Yes, your SOL once you start fighting. I'm pretty sure he had time to switch weapons at the start while healers were putting up protect and what not.
On this note though: He could've very well been working on relic and forgotten to switch weapons. I've gone in realizing the relic I'm working on is still on and switch it out quick before the runs starts.