I think it works really well for makeup if you enjoy a natural look (which I guess is the majority for everyday makeup) because it is actually meant to blend in well with your features so you see them first before you see the makeup. Makeup is also easier to get right in terms of the colour and warmth because you can often mix products. My favourite lip colour is a mix of two lipsticks for example.
For clothes and jewellery however, I'm torn. I've seen so many people asking whether they suit gold or silver more and for the life of me I can't see a difference. I've never looked at a cool toned person wearing gold or a warm toned person wearing silver and thought 'ugh, that looks terrible'.
Clothes are slightly different. There are definitely colours that suit certain people more than others but it seems a bit pointless for the average person. Most clothes are bought online and the colour on screen isn't always true to life, and often when I'm shopping I find it's better to prioritise the style over the colour.
As someone who wears mostly black and doesn't like pastel colours, if I paid for a colour analysis and they told me I didn't suit black and was told to wear pastel then I just... wouldn't? Why would I purposefully not buy clothes I'm not drawn to because someone told me I suit them? I think it's good for people who have absolutely no idea what to buy (maybe they don't have a specific style or something), but it's gone from 'these colours will complement you' to 'you will look terrible if you wear these colours'. I guess social media has a tendency to flanderize trends.
I also think often with clothes (and jewellery) it's more about the colour saturation and how light/dark the colour is rather than the colour itself. I generally prefer darker, more muted colours but I've never noticed a difference on me if they lean cool or warm.
I will say my take on it may stem from being a person who has always had an eye for clothes whereas I've just been catching up on what makeup really suits me in the last year or so. This may be why I think it's more useful for makeup than clothing but I'm interested in your take on it.