The MDR headphones actually are coloured, if you listen to them compared with other reference standards.
But in fact, ALL speakers/headphones are coloured to some degree. This is unavoidable. Your ears adapt to the colouration and become able to translate that to a generalized average of other systems youāre also familiar with.
The Adam T5Vs are well regarded here, many people like them, and theyāre on my shortlist of interesting monitor speakers. But theyāre ported, and that means while the bass sounds good, like all ported speakers it will overhang⦠the book Mixing Secrets for Small Studios by Mike Senior has a lot of detail on why ported speakers arenāt really the best reference for mixing, but it comes down to this resonance causing a sort of muddled or reverby bass compared to a non-ported speaker.
The bookās website has a list of recommended unported monitors for budget studios, although none of them are terribly cheap.
But basically, 1) colouration is a fact of every speaker, 2) all ported speakers will be very heavily resonance-coloured especially in the bass area, and sometimes at specific harmonics of the port frequency up into the midrange, and 3) speakers that donāt have these problems will either have much less bass (not a huge problem, as long as you get used to it or get a matching unported sub) or be expensive.
Edit for additional details: can you mix effectively with ported speakers? Sure! But your ears will do more work and youāll need to A/B your mix more often on a variety of systems to be sure of your bass mix. Itās an effort/time tradeoff, in the end.