Hello and welcome to the Forums to you and your flock!
You are quite correct, your parrotlet really does not need a fabric hut and they can indeed be very problematic. And as you have mentioned, they are very dangerous, both from the aspect of hormonal behaviours that they can exacerbate, and also from the possibility of chewed synthetic fibres which can cause all sorts of very nasty health issues if ingested. Quito may grumble for a few days when it's removed, but he should be perfectly fine doing without it.
Having said that, quite a few people (me included) use an alternative made of seagrass, like this one pictured below...
I ended up having to get one of these for my purple crowned lorikeet who is only a fraction bigger than a parrotlet. For reasons known only unto herself

suddenly decided that she was going to forsake her previous comfy sleeping spot and hang by her toenails from the bars on the opposite side of her cage at night, where I cannot imagine she got any sleep at all. She is THE most hormonally driven, chronic egg-laying bird I have ever seen, but because of it's open-ended construction this hut does not elicit the slightest hormonal response in her at all, although I do monitor her very closely for any change there. If Quito seriously cannot live without a hut of some description, perhaps this style might be one to consider, and it certainly is a whole lot safer
