That is mathematically incorrect.
If there is no house edge, then long term, the best the casino can do is to break even on the games. However, because of their costs (staff, development, rent, electricity, licenses etc) then they would lose money.
The reason that casinos still exist and function is because of the house edge. It is the one thing that guarantees that they will make money. Bigger casinos can afford a smaller house edge and trade on volume. ie. 0.5% of $100,000,000 is still $500,000. Smaller casinos with less volume often have a large house edge, as they need to ensure a higher percentage of their volume comes back as income.
No house edge would be brilliant for players (possibility of winning) compared to what we have now (pretty much guaranteed "losing") from a statistical/mathemtical point of view. However, any casino doing so would quickly go bankrupt unless they rigged their games