Agreed it may be a need for the crap (although what do you honestly expect?) external speaker, but as far as headphones is concerned it's far better to buy as decent/flat response pair of headphones as you can afford, and listen to the music the way the person who mixed it intended.
Also, EQ does pretty nasty things to your phase response in return for the favourable impact on the frequency balance, and there's a lot of evidence to suggest the human ear/brain resolves frequency imbalance much more readily than phase.