Kijanki, your example of a 15KHz sine wave and "three points", implying poor reproduction, isn't the case, according to the well-proven Nyquist Theorem. 20KHz is reproduced as accurately as 1KHz with a 44KHz sampling rate. As for the phase shifts from steep digital filters, this is what over-sampling was invented to address, and eases the difficulty of designing a good anti-aliasing filter. For playback 16/44 is probably better than your audio system. (As I mentioned, for recording you might want the headroom of a longer word-length.)
Bob R is correct about some amps being a limiting factor in hearing the better s/n ratios of longer word-lengths. Most high-end amps are rated as having noise levels about 100db below full power. Since amps usually have about 25-27db of gain that means that their s/n ratio is only about -75db at 1 watt, or well inside the capabilities of 16/44. Krell amps, for example, are about the best, and they have s/n ratios in the mid-high -80db range at 1 watt.
Bob R is correct about some amps being a limiting factor in hearing the better s/n ratios of longer word-lengths. Most high-end amps are rated as having noise levels about 100db below full power. Since amps usually have about 25-27db of gain that means that their s/n ratio is only about -75db at 1 watt, or well inside the capabilities of 16/44. Krell amps, for example, are about the best, and they have s/n ratios in the mid-high -80db range at 1 watt.