My guess is that the ring would be faster then the pocket space in regards to getting it out. Plus what if that sort of magic gets interfered with.
As for what Bayu said I don’t thing the doorman even knows they did with the sword as they’re probably just a normal person who guards events like this. I doubt he even knew they had the pocket dimension. Hades maybe he’s in on the attack that totally won’t happen and he wanted an excuse to make her be unarmed for said attack that definitely isn’t going to happen.
The doorman actually doesn't care... And as far as he is concerned the "Guard Duty" of the girls is a polite joke.
The girls are basically fancy ornaments suited to escort High Ladies to the restroom, and not much more.
They look, act , and behave like "proper women" who cannot possibly be a threat to anyone, especialy a male. Any kind of weapon would be a fancy prop, and she might actually hurt herself using it. She listened to him like a Proper Woman, and got rid of the dangerous thing before she could hurt or embarass herself.
It's that kind of world...
He may have heard rumors of her winning the Tournament, but that must have been luck, or one of the Nobles with an eye on her decided to spoil and amuse her and rigged the tournament, or...
Any number of reasons why she's still underestimated, and her accomplishments aren't recognised.
Yes, I know... An assassin's wet dream... Which is why the "Poisonous Flower" is not a mere literary trope...