Higher insurance correlated with higher BHP, is it a myth?

In the absence of being able to analyse such significant amounts of data, insurance estimates were based on more 'common sense' factors alongside what could be derived from historical information.

The amount of data recorded and in a state that's able to be incorporated in to the premium calculations now means that 'common sense' is utterly irrelevant, and it is far more accurately tied to the statistical reality of historic claims etc. Except for gender of course as the statistical reality that men are likely to cost the insurer more than women was deemed sexist.

EDIT:
Some good examples of reality not matching 'common sense':

Parking on driveway less risky than parking in a garage, because people tend to hit their garage and have to claim.
Third party often more expensive than fully comp, because people who go third party only are more likely to claim (under the assumption it's cheaper).
Paying monthly more expensive than up front, but not just from a finance perspective, but because of the claim profile of those who pay monthly.
Arranging your insurance weeks in advance is cheaper because the profile of those who do is less risky.

Anecdotal, but I think once you get beyond a few modifications, it actually makes no difference or potentially becomes a bit cheaper if you have a full on shopping list of changes, again because those that provide so much detail tend to fit a different risk profile.

I think it used to be a major factor years ago, but isn't so much now.

It seems to be more about how prone certain newer models are to getting stolen, and while higher powered models still feature like Audi RS, BMW M and Mecredes AMG feature quite highly so do Range Rovers.

And EVs seem to have got expensive to insure too.

But older cars seem to be completely different. In 2019 I had a BMW 3.0Si Z4 Coupe with a couple of modifications and replaced it with a Z4M Coupe with a few more modifications and another 80BHP, but my next renewal was cheaper than what I had to pay for the 3 litre.

(And I have a theory that what’s actually happening is that higher risk cars tend to be bought by higher risk drivers, rather than that the cars are inherently risky - I suspect that a hypothetical 20 year old who had a Golf R because for some reason it was the only car available and didn’t give a toss what he drove would be less risky than one who was living on beans on toast just to have one. Modern bread and butter cars have the performance of 80’s hot hatches without the insurance loading)