"ECB is hiding or misrepresenting the real rate of inflation." ECB has no role on that, which as I said was in favour of including house prices in the HICP. It is the European Commission deciding on that: https://ec.europa.eu/eurostat/web/hicp/faq

Please note that "H" stands for "harmonized", and that is one of the issues. If you change how the HICP is defined, then all the countries should produce the new indexes that should be included, with the same methodology. That is a challenge and a national political issue too in some cases.