These are called "mIRC Colors" for a reason; mIRC innovated it. I wager that IRC clients that support mIRC Colors use the same color tones for the 0-15 values. Not all clients support the same color tones for 16-98 but many of them have begun to in the past few months with only one or two notable exceptions of resistance. (ie, IceChat). Some older clients might just recycle the 0-15 colors over and over from 16-31 and 32-47 and so on.
The colors that were chosen are based on hue, saturation, and luminescence values which are the same for each row or column.
On a side note, I would not be against mIRC supporting multiple pallet types. Some people have expressed a desire to make all of the colors more muted or shift them to lighter or darker shades based on their background color and relative intensity. Other users might want to switch to IceChat's colors if they mostly interact with other IceChat users. So selecting between pallets might become a thing someday, or not.
