Bass comes with distortion so you can't elevate bass and expect no penalty for it. In this case EQ is a trade. You weigh the pros and cons. Sometimes getting more of muddy bass is not your preference. Leakage from long hair and glasses can worsen it. People tend to say that distortion doesn't matter in headphones, but they really mean that within reason. Distortion at bass can be very high and if you add to that leakage it means that your driver has to wobble outside of it's linear region. Such was the case of Sennheiser PX100, which had speaker level of distortion in the bass and consequently lacked the clarity of it's direct competitor, Koss Porta Pro. It's worth noting that the Koss generally sucks in it's upper range, which is why I personally never respected that headphone either.

Midrange and highs can have problems related to phase and personalisation. They often have very sharp peaks that drift in frequency from person to person. Good luck with notching them accurately! That's because the frequency of modes in the cavity between your eardrum and the driver varies with volume. If you have wider head, the driver will be pushed closer to your eardrum. If you have bigger ears, they'll displace more volume. Your ear canal entry can vary too.If you study B&K 5128 patent, you'll see that there is no one ear impedance. There is a range of ear impedances. That's OK for broad humps. Not OK for undamped resonances.

Back to the peaks and nulls in the highs. It's not easy to fix them and sometimes impossible when the mode is out of phase and cancels the otput from the driver. In such case the sound literally cancels itself and no matter how much you crank the volume up, it still is near zero dB. The only remedy is to physically address that mode in the earcup or the driver. A null like that will result in decreased detail and is an example of non-minimum phase behavior in headphones that is usually not talked by reviewers such as Crinacle, because it makes the topic too convoluted for non-engineers.

Sample variation can be an issue. You need the manufacturer to have at least some decency and do consistent QC and driver matching. On top of that the driver has to have the potential to compress air at low frequencies and have optimised modal behavior on both sides of the earcup.

That being said there are some cheap headphones that do most of that well. Long forgotten Philips models that are still in circulation on used market can be EQed to some success, but you need to make your own curve and I think this is the most important part - nobody cares about cheap headphones enough to work on EQ for them. They suck in more ways than just sound. Build quality and comfort for example. Some of them do one thing well. Aiwa Shellz comes to mind :) Can you make the upper range beautiful on those cute little buggers? Absoulutely. Can you make it play bass? Absolutely not.All in all when you EQ a headphone, it's better to be on the safe side and only add low Q filters. You'll avoid making things worse.