Sure, legalizing it would cut out the parasitic "mafia", but would introduce a NEW parasitic "mafia"... The government.
Payroll taxes (Fed tax, State tax, Social Security, Medicare, etc) are probably 15-20% right off the top. Then you got to add in the medical component... which in the US is exhorbitantly expensive. Then, you know that if brothels were legalized, the government would need to set up some regulatory agency to "license" and "inspect" them. This would entail fees, as the government won't issue you any license, form, or inspection certificate unless you pay fees. On top of this you would absolutely need insurance. When you do the brothel "under the table", if someone gets sick, gets hurt, catches an STD, etc.. you could just tell that customer to stuff off, or if the heat were high enough you could move. If you run a legal brothel, insurance liability would, in my opinion, probably be through the ceiling.
As you say, you would still need to pay the receptionist... but before you cut off the pimp, perhaps you should first consider the services that the pimp provides. The pimp does your marketing, and provides security. If you are running a legal brothel, you will still need to market your services, and you definitely need security and protection. Because the law probably frowns upon individual armed "enforcers" preserving security through intimidation, you would instead need to hire some legal security service, and I would venture a guess that these services are also fairly expensive.
There are differences in the physical overhead cost structure as well. If you are running under the table, you can run a brothel out of any old structure, office space, storefront, or residence. If brothels were legalized, the physical structure would need to meet commercial real estate code... in the US, this entails ensuring proper fire supression systems are installed, access for disabled people, etc.
So... I'm not really sure if it would be cheaper or not.