Hey,
my husband’s aunt is severely allergic to dust and had the carpet replaced with laminate specifically because she thought she would cope better that way.
Well, shortly afterward she was already annoyed because now the dust flies around much more than before with the carpet and she has even more problems with her allergy.
By the way, in the new house we also have carpet in the bedrooms + dressing room in combination with underfloor heating (however, no high pile, but short loops) and are wonderfully satisfied with it.
Simply vacuum over it quickly, instead of having dust accumulations everywhere flying around. Even my husband, who was previously rather skeptical as an allergy sufferer and a fan of smooth floors, likes it wonderfully!