I think, you are wrong. Of course frequencies do have confidence intervales. Frequencies are the estimate of the probability of the occurence of that class which number of occurencies in the sample has lead to the calculated frequency. The sample is random, and therfore the estimate from the sample is also random. The clopper-pearson-Interval is used to calculate the upper and lower bound of the confidence interval for the estimated probability.

If you have a dichotomous variable than a descriptive statistic of your concret sample is the frequency. However if you want to generalise your result to the whole population, than you take the frequence as an estimate for the probability. This value is random and as measure of the uncertainity a confidenc interval shoul be given, which is the clopper-pearson-interval.

If you have a metric variable than a descriptive statistic of your concret sample is the mean. However if you want to generalise your result to the whole population, than you take the mean as the estimate for the expected value. This value is random and as measure of the uncertainity a confidenc interval shoul be give. For normal distributet values with unknown variance these are calculated with the quantiles of the student distribution.

Frequencies and the lower and upper bound of the clopper pearson interval are always positive. Therfore it makes sense to use a bar-graph with added confidence interval.

Means and there lower and upper bound of the confidence intervale could be negative or positive or embracing the zero, there it might be better to use a dot-plot.