Another way to look at this question is to ask how the players who are eligible for the title rate the title compared to other titles as reflected in the take-up rate.
Every month FIDE publish files of rating data for all current FIDE registered players which also includes details of the titles they have. From these files it is possible to extract counts of how many players in different rating ranges have which titles.
Doing this for the December data gives these results.
First the number of players with each of the different titles (I'm just looking at "open" titles rather than women only titles).
GM - 1647
IM - 3762
FM - 7869
CM - 1663
The first thing to note is that the higher the title the fewer players have the title, with the exception of CM. There are only a few more CMs than GMs.
Next, since probably a significant number of CMs got their title by a tournament performance rather than reaching 2200 ELO, try and get an estimate of how many players got the title by rating.
Since the FM title works in a similar way I will compare the two. A player can reach the required rating for a CM or FM title and get the title for life but as they get older and weaker their rating goes down. So, I'm going to look at the number of titled players above a floor 200 points below the required rating.
The number of FMs with a rating of 2100 (=2300 - 200) or over = 7244. This is less than 10% down on the total number of FMs = 7869.
The number of CMs with a rating of 2000 (=2200 - 200) or over = 957. This is more than 40% down on the total number of CMs = 1663.
Next I'm going to look at the number of players who are eligible for the CM title by rating but have no title and do the same for the FM title.
Number of players rated 2200 or over = 21047.
Number of players rated 2200 or over with no title = 9665.
So, about 45% of the players who are eligible for the CM title don't want it badly enough to apply.
Number of players rated 2300 or over = 8750
Number of players rated 2300 or over with no title = 1513
So, about 17% of the players who are eligible for the FM title don't want it badly enough to apply for it.
If you narrow down the range for the CM title to only look at 2200 to 2300 (so, eligible for the CM title only) then you get -
Number of players rated between 2200 and 2300 = 12297
Number of players rated between 2200 and 2300 with no title = 8152
So, about 66% of the players who are eligible for the CM title and not eligible for other titles are not interested.
Overall those figures tell me that players who are eligible for titles don't rate the CM title anywhere near as much as other titles.