Thats not true. The cost of the checkup are covered once before you turn 35 and every three years for anybody above the age of 35 [1]. Still, people have to be willing to do that checkup, make an appointment by themselves and so on.

Still, seeing what is and what isn't covered by public health insurance just seems so stupid. The focus on cure instead of prevention, and that not even particularly good. It's sad to see how much money goes to waste for useless treatments with something like homeopathy while people who really need proper treatment are stuck with the cheapest option that is paid for.

[1] https://www.bundesgesundheitsministerium.de/checkup.html (German)