There are a lot of more technical limitations that just don’t really change based on frequency response tweaks. However, tonality is a very big part, and you can often adjust a bad headphone quite a bit with EQ before you start getting distortion, and it really does turn into something good, though I’d argue it won’t get to great.

Ultimately, you can have 2 headphones that essentially measure the same, but still sound/present the sound quite differently.

The absolute best value approach in my opinion is to get a headphone in your budget with the best technical abilities/detail and presentation style that you want, and then “fix it” with EQ.