This kind of cultural take relies on a weird essentialism that's probably better explained by political economy. The only place that can really be said to have a strong connection to kickboxing that rises to the level of culture is Thailand. In other places such as Holland or other parts of Europe, there have been investments in the promotion of kickboxing events that were a bit more significant than the history of the sport in the US, but it's still not even in the top 10 most watched sport in any part of Europe, much less most participated in. In that sense, it's somewhat similar to wrestling in the US except wrestling is integrated into scholastic programs here that mean exposure at a relatively young age for a continuous period of time whereas kickboxing has no analogue outside Thailand. Further, even in the absence of kickboxing, there has been a predilection among some Americans to take up other striking arts from childhood and the ISKA types were doing full contact stuff, though the investment was drying up in the 90s right when NHB came on the scene to absorb any people looking to turn fighting into a career path. There were more connections here between striking arts success and Hollywood in the post Bruce Lee era than there were between professional sport. This isn't a cultural issue so much as a material issue. Further, MMA gyms in the US have imported many of their best trainers in disciplines like BJJ and kickboxing.
I'd say what this is indicative of rather than any cultural disposition is that MMA grew up as a truly global sport in a period of intensifying globalization. This means the idea of best fighter "in the world" holds a little bit more weight than it did in some other sports that are hyperlocal. It was really the consolidation of American, Brazilian, Russian and Japanese promotions under the relative monopoly of American companies like WME/Zuffa and Viacom that gave us this modern instantiation of MMA. Also, due to regulatory issues here in the US and financial woes, the UFC in particular was incentivized to expand around the globe to build market share, relying heavily on media deals to keep the company alive at various points and thus investing in building pipelines for non-US talent to develop. In the US, the main gyms that grew to feed fighters to the top promotions remained wrestling or BJJ based (usually with some form of a striking trainer on staff in an attempt at hybridity) because those styles had more established roots in the earlier version of the sport and in some cases more formal ties to the investors that allowed the UFC to continue doing business e.g. Flash Entertainment, USADA, the Kingdom of Bahrain, etc.
Tl/dr: as you allude to, it's the gyms and individuals, not the traditions, but it's also the history of the sport's development and where/how money was invested.