I noticed this same problem with Audacity a couple of years ago. Stopped using it for resampling because of it.
In the back of my mind, I recall copying files from my Linux PC to my windows laptop and doing the conversion there, for some reason it worked better. Maybe a newer version of Audacity on the Windows at the time.
If I recall, I think it's not quite so bad if you do it in multiple steps. Like:
load 24/96, save as 16/96
load 16/96, save as 16/44.
Now I use a program called "ssrc" which is a commandline program. I'm probably the only one here who uses it. Free software, open source, runs very slowly, but seems to do a superior job. If you can compile C code on your Mac.
http://shibatch.sourceforge.net/