So apparently KW averages mid 30s against Australia, England and India. Bloke is one of the biggest minnow bashers and HTBs in cricket but seems to have largely escaped scrutiny for it. Because he plays for NZ and not a higher profile country?
Will try to answer your specific question and not get into debates around why labels such as HTB are understandable, but seem a bit simplistic (my view anyway).
As to why he may have escaped scrutiny (and I don’t believe this is the case at all actually - everyone around me in India who cares is more than familiar): in the first half of his career, say till around 2017-18, NZ played tests more frequently abroad, enjoyed a pretty reasonable run and generally forged a reputation as a more competitive touring team than most. Williamson put in some really good performances here which were often, but not always, instrumental in NZ doing well in countries they were previously losing badly in. Examples:
Century on debut in Ahmedabad 2010, which was a huge achievement for a 20 year old, a 138 which helped win at the P’Sara test in 2012 (Ross Taylor was infamously dumped as captain after this), some excellent batting when NZ won 2-1 in the Windies (this was one of those series Windies actually played very well), the centuries at Gabba and WACA in 2015, and, probably his most underrated feat , a great record in the Pakistan’s fortress the UAE especially in the series decider in 2018. Also a century at Lord’s in 2015 which is always good for visibility. All this definitely left an impression on people who were used to the NZ of the late 2000s, and may have put lower scores in the shade.
Since then it’s been diminishing returns for sure, and some criticism is certainly deserved. But I will say that unlike the other three who generally come up in this conversation, playing 2 test series 5-6 years apart makes it a bit harder to bridge the gap. And the opportunities against countries outside the big three are even fewer - NZ haven’t toured the Windies since 2014, South Africa since 2016, Sri Lanka since 2012 and then 2019, Bangladesh since 2013 and then 2024 etc. Maybe you have to play a lot more for the scrutiny to keep up?