So, I tried a zero-inflated beta model (beta because data lies in the [0,100] interval, and so I just divided by 100).
The estimates I got using GAMLSS showcase a very low $\nu$ estimate, i.e., the probability of a zero occuring. So, essentially, it just fitted a standard beta fit, a bit like this one on the top right corner:
Why does it do this? How can I fix it? What other distributions are there?
My data clearly DOES contain zeroes, many of them, so a standard beta is not a good fit.