ASIO was designed for recording. Back in the 90's Microsoft's available drivers could not be used in a professional studio - too unreliable. Can you imagine paying a studio in which you (the talent) had to redo a take because the computer randomly inserted a pop/click/tick/drop-out in the middle of a recording? ASIO emerged as the solution, and the the Window's recording community hasn't needed to look elsewhere since. (Mac's Core Audio is effectively the ASIO version for Mac, sorta)
Until WASAPI, ASIO was enticing for playback because it was strict with handling sample rates. ASIO doesn't do sample rate conversion. If ASIO-compatible software app (music, etc.) wanted to playback 88.2k, then ASIO would tell hardware (DAC) to use 88.2k. However, ASIO was intended to work with ONE software app at a time (perfect for recording), while Windows wants to mix all the possible streams (insert Ghostbusters: "don't cross the streams"). :) Of course, WASAPI has exclusive mode, per Dr. Spengler's advice. :)
At this time, I'm not convinced ASIO is great for playback. For recording, ASIO (Windows) is the only way to go.