I don't know the experience you having with wired headphones / earphones and DACs. The important word in your post is "significantly". Yes, is possible obtaining better sound with a good DAC but this benefits in reality are (very) small, but is often common finding very exaggeration in many posts, specially when the DAC, amp, cable, portable player is (very) expensive. This is common with all audio equipment, the exaggeration that producing many better sound with DACs, amps, expensive hi-res portable audio player, burn-in, hi-res files and cables...and is the same exaggeration with many better sound from (very) expensive headphones or earphones.