You could of course build a model for each different group, there is nothing wrong with that. However, you'd require larger sample size and need to manage multiple models.

By using mixed model, you pool (and share) the data together and thus require smaller sample size.

In doing so, we are sharing statistical strength. The idea here is that something we can infer well in one group of data can help us with something we cannot infer well in another.

Mixed models also prevents over-sampled groups from unfairly dominating inference.