DACs are an enormous part of the sound.
Headphones are just speakers. They don't actually make the sound on their own, they're just there to transmit the bits of data being fed to them after it's been translated into analog. It doesn't matter how amazing your headphones are if the music being fed to them is bad or the signal is weak. You can throw FLAC files at a crappy source without enough output power all day long and it's never gonna sound any better than those 128s.
Remember, everything you listen to through your headphones comes via a DAC and an amplifier. Everything. The question is whether the INTERNAL hardware on whatever source you're using is adequate. Plugging your headphones into a Mac Pro is going to yield a wildly different experience than plugging them into a $200 Chromebook. Suggesting that DACs and amps are unimportant is foolish. It'd be like making a car audio system in your 1987 Civic and acting like you can still keep the stock dash unit an expect everything to sound great.
Imho the difference in sound quality between well-implemented DACs - of which there are many in various price ranges from budget to extremely expensive - is rather small compared to the difference switching headphones or amps will give you. It's pretty simple to design a well-implemented DAC too, when compared to amps and especially headphones.