Cheap 'phones sound like cheap.
Good, and there are some inexpensive GOOD 'phones, don't sound cheap. They sound GOOD. And the better they are, the better they sound.
Just got the Loaner Cosmic today. Definitely not a cheap amp, but combined with my Senn HD600's, the sound is "Touchable", palpable, incredible.
Bass that can almost be felt, the Brubeck Quartet spread out in front of me, and Paul's sax sounding like he's playing it for ME. And that's not a very good CD as far as its overall quality is concerned.
Harmon Kardon FL8300 CD Player, line out to Cosmic, to HD600's. I know that it gets better than this, but I don't ever want to actually experience it. My wallets inside out already.
Seriously, if listening to music is important, if QUALITY sound is important, read the various threads about different 'phones. GOOD 'phones make good sound, and there ain't no other way to get there.