Number of segments does give an indication of how far away the common ancestor might be, but it's not as accurate as total cM, so the latter is more often used.
A parent/child relationship share 23 segments since each segment is a chromosome. One generation further and the average number goes up to about 28.5 segments because each chromosome has about 37 crossovers and your matches are now shared by 2 ancestors. Look at the avg segs/anc column in Jim Bartlett's table from his Crossovers By Generation article:
You can see the Shared cM column reduced by a factor of 4 for each generation but the average segments per ancestors goes down only about 40% per generation, so the total cM provides more accuracy for estimation.
However, there is a very good use of number of segments for close relatives. The total cM alone cannot differentiate aunt/uncle/niece/nephew from grandparent/grandchild from half siblings because they fall in the same total cM range. But their number of segments tends to differ. Kitty Cooper wrote an article Half sibling or Nibling? and plotted number of matching segments versus total cM:
There is a third criteria worth using as well, and that is the size of the largest in cM. Kitty Cooper talks about it in her above article. And Lara Diamond writes that for endogamous populations, the largest segment size is possibly as important if not more important than total cM to identify closer relatives.