In one way, I do agree with you, though I would like to bring my point of view forward.

Let me use Codeforces as an example, since you have compared Codechef to Codeforces.

Notice the contest duration difference between Codeforces and CC Long Challenges. A typical CF contest is ~2.5 hours, whereas a long challenge is ~240 hours. Quite a gap right? Now notice the number of successful submissions for the hardest problems in the set **during** the CF contest.

In a span of 2 hours, multiple people have managed to correctly solve all the problems in the set. If the problems in CC longs were mainly algo and DS based (like most CF problems), eventually many would solve nearly every problem in the set. Whats the point of competition then? No one would even have substantial rating changes then, leading to people slowing moving away from CC.

This is why math based problems are included. The amount of time provided is sufficiently enough to reduce the problem to an equation and research on the best method to solve it. Most of the people just give up once they realize it requires math, as they simply want a straightforward implementation problem.

With the time duration of the contest, one could easily make testers, generators and observe patterns, thus finally reaching the answer.

Also, its not like all the questions are complete math based - they do include some algo and other related stuff.

Regarding the number of contests conducted, CF has a bigger, more active user base than CC. This is one of the main reasons for the difference in the number of contests.

Summing it all up, we really need to appreciate CC for its novel 10 day coding contest. TBH, most of my cp learning has taken place during these wonderful contests. Also, if you have medium~hard problems requiring little to no math, you should really apply to become a problem setter. Only then you would realize the amount of difficulty present in making a pure algo/ds problem to engage many participants over the 10 days of the contest.

In any case, COOK-OFF and LTIME is conducted every month with most problems requiring little math knowledge. So in my opinion, LONG contests are mainly for learning new stuff (so what if it is math, it is still educative!) and short ones, like all other short contests, are for ioi/icpc aspirants.