If you get an individual fibre bundle and handle it, the individual fibres that make up the fibres can fluff up relative to each other.
This means they either need to be set in resin or they need to be protected in other ways. Set in resin it is not really very clever with abrasion however we often need to protect carbon from abrasion and do successfully with other materials.
Whilst it is true that carbon suffers when it is forced to take high loads in tight radii.
The thing is your waist, even if you are a child, isn't a tight radius in engineering terms.
As an example I have taken the entire primary rig loadings of a 40′multihull yacht through carbon bent to a radii of 2″ successfully.
Even if you look at the fibre deflection in weaves to make commercially available fabric the tow clearly takes a radius.
Furthermore a belt has loads that are not in any way taxing. A single stand of 12k Hexel IM9 carbon tow with a cross sectional area of 0.18mm is good for about 118kg.
In fact there is no reason why you couldn't use it to make a belt or weave it into your own belt.
In fact it is so useful as a dry structural fibre that it is used as the load carrying element of some of the most expensive sails on some of the biggest and fastest yachts and superyachts.
It is set between two sheets of plastic like mylar to make a smoother surface that is also wind proof. These need to bend and roll, avoid chafe etc and do successfully.
The round the world yachts frequently use them do the material is durable. If you visit a sailmaker and ask him to make a belt with offcuts I can't imagine it would be taxing.