Currently, when you carry out task Foo, you perform steps A, B, C and D. Regulation is introduced which says you cannot under any circumstances omit step C.
Even if no one is skipping step C, the enforcement mechanism requires auditing. If there exists an alternative to step C, is it compliant with the regulatory requirement? The regulation itself introduces legal risk which needs to be mitigated. So yes, it increases expenses.
Those expenses are on the part of the regulator, which is funded differently. As a society, we may be paying more to say "you must do step C", but as a customer or provider of Foo, there's no change.
No? Entities don't get to write off the cost of being audited, there's a very real expense associated with both documenting the regulated process in a compliant manner and working through the audit process with the relevant regulatory body.
No increase in expenses.