When you know you're going to release something in a 16-bit format, it makes complete sense to record 24-bit, and do all your processing with that increased level of precision before you set your final levels and dither the signal down to 16 bits.
However, it makes no such sense to record at a higher sampling rate (sampling frequency) unless you have some evidence that your particular signal processing chain works better that way--a conclusion which would require careful testing. In general it shouldn't be expected; there's certainly no theoretical reason to expect it. Sampling rate and bit depth are entirely different things.
It could be an advantage in a particular case, due to some shortcoming of a particular 44.1 kHz converter, for example. But if that were a widespread situation, then recording at 96 followed by conversion to 44.1 ought to sound distinctly better to the people who prefer 96 kHz recording than recording at 44.1 in the first place sounds. In general that doesn't seem to be true.
Think this through with me, please: When you sample at (say) 96 kHz, the signal components below 22.05 kHz aren't recorded any more accurately than they are recorded by sampling at 44.1 kHz. But the filtering occurs at 48 kHz instead of at 22.05, and even though no one can hear between 22.05 and 48 kHz, the signal components below 22.05 kHz may be handled in a more linear fashion. Such is the rationale for 96 kHz recording in a nutshell.
Unfortunately, when you then convert down to 44.1 for release, you must filter a second time (at 22.05 kHz) to avoid aliasing distortion. Signal components between 22.05 and 48 kHz can't be allowed at that point. So in the end, you put the signal through more filtering--not less--by starting out at a higher sampling rate. The entire approach is self-defeating in that sense.
--best regards