This is the case in the vast majority of the cases.
Just remember that the added liquidity is the price of your privacy,
It's not that DEXs are dearer; the centralised exchanges offer discounted spreads because they thrive on selling your data to very nosy actors.
Apart from the fact that they have very expensive service fees, which is why we often hear that using BTC is too expensive, it seems that data harvesting is a real gold mine where they make money. It doesn't have to be CEXs doing it at the highest operational level, but one corrupt employee is enough for the user base to become public.
CEXs are unfortunately a necessary evil, although alternatives exist and people should use them more.