From what I know, the higher end phones don't suffer from burn-in. Your phone is quite cheap and they do have to skimp on something. It's generally a good idea to get a midranger with an LCD instead of OLED, for that reason. You lose some image quality but you avoid these issues.

Moto Z cost north of 700 €. I would not call that cheap.

Well, considering how much an iPhone XS costs, the definition of "cheap" for a smartphone has migrated North the past few years :)))