Headphones or loudspeakers can change the "personality" of a system in exciting and fun ways, but can never repair or correct damage done by upstream components to the delicate music signal. And they can't "fill in" musical detail that the dac is not providing.
Since a dac is dealing with voltages that represent numbers and an analog amplification stage, both can be easily corrupted. "Bits is bits" doesn't work in real music systems, and the 73 cent dac in my phone does huge damage to the music signal compared to say, a $500 or $2000 dac designed for high fidelity systems.
For me, the "sameness" in the sound of dacs fades once I move away from the standard frequency response comparisons (brighter, etc), and listen to the music. True timbre, texture, and touch, graceful and natural dynamic flow, real instruments in space, the perception of hall sound even in "silence", are obvious.