I agree, that for most calculations those details are unnecessary and can be avoided. However, existence of something is not depended on it necessity for us.

Moreover, AFAIK (I'm not a real scientist, so beware), Higgs «field» and medium for gravitational waves (g-medium?) are two different mediums, because Higgs boson is spin-0 and it gives mass, while graviton is spin-2 and is massless.