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It depends on the bead to bead distance for the tyre. Some 23mm tyres are not really 23mm are they. I personally like tyres that bulge a bit. That protects the rim and its more like the tyre shape the manufacturer intended. Tyres that are over stretched do feel a bit more skittish. A bit of sidewall flex is desirable.
The first time i used a 25m gp5000 tyre i fitted them to 20mm internal width ailerons and the centre of the thread wore thinner than the shoulders when i pulled it off after holed.
I am quite picky with tyres.
I've got some wheels with Belgium Plus rims which I run (sometimes) on one of my bikes with 23s. Never had any issues. In fact, they work very well.