Among dps characters, some ascend with crit rate and some ascend with crit damage. By default most characters start with 5% crit rate and 50% crit damage. Crit rate characters can reach 24.2% crit rate at level 80-90, whereas crit damage characters can reach 88.4% crit damage at level 80-90.
From these base values alone, crit rate characters have an inherent advantage over crit damage characters. The formula for expected crit multiplier is $$x = 1+rd$$ where r is the cr and d is the cd. For crit rate characters (without weapons, artifacts, etc.) they can naturally get 24.2% cr and 50% cd, so \(x = 1+.242*.5 = 1.121.\) By contrast, crit damage characters naturally get 5% cr and 88.4% cd so \(x = 1+.05*.884 = 1.0442.\) In other words, without extra weapons/artifacts/passives/supports buffing the character, crit rate characters can naturally have a higher expected crit multiplier than crit damage characters (the difference is roughly 7.4% more).
Sure when you crit, the number may be higher if you have higher crit damage, but what's the use in having high crit damage if you can't crit in the first place? That's why having crit rate is important.
Recall formula for expected damage is $$E(Y) = (1-r)x + r(1+d)x = (1+rd)x$$ given crit rate r, d and base damage x. So the damage Y is a bernoulli variable $$Y = x(1+dBer(r)).$$ The variance is just $$Var(Y) = x^2 d^2 r(1-r).$$ This is for one instance of damage.
So what if you have multiple instances of damage? Say there are hits \(Y_1, Y_2, Y_3, \ldots, Y_n \) each with fixed crit r, d. Then each of these are Bernoulli variables with say base damage \(x_i\) $$Y_i = X_i(1+dBer(r)).$$ We assume they are independent and identically distributed (iid). The sum of damage is $$Y = \sum Y_i = (\sum x_i)(1 + d^2Ber(r)) = X(1 + d^2Ber(r)).$$ The variance of this is $$\sigma^2 = X^2 d^2 r(1-r)$$
The average damage (sample average) is $$\bar{Y} = Y / n.$$ The variance of this is $$s_n^2 = Var(\bar{Y}) = X^2 d^2r(1-r)/n^2 = (\sigma / n)^2.$$
As \(n \to \infty\) the sample variance \(s_n \) above goes to 0. So the more hits there are, the closer the average damage is to the expected damage. In other words, one big nuke will have more volatility in damage (can miss the crit), whereas dps that is split into many parts (like Xiao C6 E, Dehya Q, Scaramouche C6, Scaramouche Q, Cyno C6, Cyno dustbolts, etc.) will have less volatility and tend closer to the average expected damage.
The above is related to the law of large numbers (LLN), where the sample average tends to the expected average of the underlying distribution as the number of samples approaches infinity. The LLN applies here as we are dealing with iid Bernoulli variables with finite expectation and variance (they are discrete and Lebesgue integrable using simple functions). Specifically, we can say the 'strong' LLN applies and that the sample average converges almost surely to the expected value.
Another key theorem in probability is the central limit theorem (CLT), which states that the distribution of the sample average approaches a gaussian in the limit of large n. As we are dealing with Bernoulli variables, the sum of Bernoulli variables is a binomial random variable. Then the special case of the CLT, the De Moivre-Laplace theorem applies. Specifically $$\frac{1}{s_n} \sum_i (Y_i - E(Y_i)) \to N(0, 1)$$ converges in distribution.