What you write is true however the sort of test you describe for Germany and Italy is not counted in the statistics at all. All those free PCR at airport and free antigen are not forwarded to health authorities, so do not appear anywhere.
Then there is the qualitative value of those tests. SWR (a news media in Rheinland Pfalz) manages to get a truly staggering information via months of inquiries: there was nearly 2 millions tests done via those antigen test center or self test, and they found 740 positive people, which is a very low return, during May where the prevalence was still significant.