"flat" and "neutral" are 2 different things.

Classical music are acoustical instruments and most of them are in the mid range.
A headphone with a V-shaped frequency response I do think totally unsuited for classical. The thundering bass masks the midrange. That piercing treble you won't find in real life. Go to a concert hall and listen to a symphony orchestra. Notice that you can hear contra bass and kettle drums but also note the level is low. Like wise a Steinway. Very big but very soft on the bass.
Basically, use EQ to tune your headphone to obtain a neutral response.

What is neutral? Often the Harman or the Sennheiser response is mentioned. Harman did some excellent research. They even found out who didn't like their curve. Bass heads think the bass to soft. Woman think the bass to loud and people over 50 think so to.
Evidently, it is a preference. https://audiosolace.com/harman-target-curve-explained/

Best you can do is calibrating your hearing. Visit live performances, preferably in a hall with good acoustics. This wil be your reference.
My practice is a sober one. Using Etymotic ER4P I boost the 100 Hz band with2-3 dB. Using HD800 I do exactly the opposite.