California, USA is one place where you see these posted rates.
I believe this is to comply with Civil Code Section 1863:
(a) Every keeper of a hotel, inn, boardinghouse or
lodginghouse, shall post in a conspicuous place in the office or
public room, and in every bedroom of said hotel, boardinghouse, inn,
or lodginghouse, a printed copy of this section, and a statement of
rate or range of rates by the day for lodging.
(b) No charge or sum shall be collected or received for any
greater sum than is specified in subdivision (a). For any violation
of this subdivision, the offender shall forfeit to the injured party
one hundred dollars ($100) or three times the amount of the sum
charged in excess of what he is entitled to, whichever is greater.
There shall be no forfeiture under this subdivision unless notice be
given of the overcharge to such keeper within 30 days after payment
of such charges and such keeper shall fail or refuse to make proper
adjustment of such overcharge.
I assume the intention was to prevent things like price gouging for distressed travelers, special events, or customers the management sees as undesirable (e.g. racism). However, as you point out, hotels often set this rate very high, so that they can charge high rates when they want, and claim everyone else is getting a discount.
Given this, I'm not sure why they stop at prices that are 3-5 times the actual rates; why not post a rate of a million dollars per night, and have complete freedom? There may be some additional regulations that I don't know about.