Czechia made it mandatory because government made really huge mistakes in first 2 weeks* and they are scared and panicking because health care system is underfunded for long time. There is no reason to wear mask in every public space as everything except centers of big cities is empty during lockdown. It makes sense inside but not in parks and empty streets. It just forces people to waste masks which are not in huge supply globally.

* In February prime minister forbid hospitals to buy face mask and decided that he will buy them centrally and than distribute them to hospitals. In the begining of March when coronavirus appeared in Czech republic he also sent finacial control against face mask importers to ensure that they are not selling anything. He wanted to look as savior of the country but he wasn't able to buy any masks so for 2 weeks there were only 10 000 mask from reserves for the whole country. People started to sew mask at home and partially saved situation. After that prime minister made wearing mask mandatory which in my opinion is mainly PR to make the home made masks look like his own initiative. He also spreads fake news about Germany, Austria and other west European countries saying that they are not responsible and that they just copy Czech measures when it is too late. But in reality his administrative is really struggling without any plan and his main efforts go to PR.