I am running brms models with flat prior using several different types of data, just to train, I am learning^^, and each times I run the simplest model - means without random effect and only with a factor as fixed effect -, I have a problem of variance not taken into account by the model.

This is what is happening when I plot pp_check intervals:

The model is simply set as brm(response~factor,…)

Is it because brms doesn’t work without random effect in the formula?

The plots looks reasonable to me. Without modeling overdispersion, you will not see correct calibration in the plot with your data. To add overdispersion use, for example

Yes I thought about this too but then I run normally distributed data with gaussian family and the same problem is happening. I might be wrong but we should not have problem of overdispersion with normal data.