Why don't we just let the price of stamps rise to where it makes sense, instead?
Because that would allow the USPS to continue operating smoothly, and is thus illegal.
The goal of both parties of Congress is to sell off the lucrative USPS to private interests. In order to do that Congress and its owners must trick the public into believing their valuable USPS is a failing, worthless business.
The USPS cannot - by law - raise the price of stamps by anything more than the "rate of inflation" the government announces. The Consumer Price Index (CPI) is a politically-motivated number, since higher rates of inflation reflect badly on politicians and cost the government money in payments keyed to CPI. So the USPS is legally prohibited from raising prices to reflect its costs, and even the amount it is allowed to increase is artificially low.
The USPS is prevented from doing what every other business is allowed to do - change its prices to reflect changes in its costs - and then the results of this Congressional restriction are used in Congress as an example of how the USPS is inept and inefficient and must be privatized!
This legal constraint on the revenue side is matched by a legal requirement for the USPS to wildly increase its expenses. The same law restricting increases in USPS revenue requires the USPS pre-fund 75 years worth of retiree health benefits - while private businesses are being allowed to completely renege on even existing pension agreements.
(There's also a little backstory here about Congress mandating these huge front-loaded payments. The USPS had been overpaying into its pension fund and was actually going to be able to reduce the amount it needed to pay, but because of unified federal budgeting, USPS payments into its pension fund counted as revenue to the entire government. Congress required these huge payments from the USPS to make sure Congress didn't have to reduce its own spending. But that's a detail, like robbing a person already being murdered for their bodily organs.)
The goal of this simultaneous restriction on revenue and increase in costs is to force the USPS into bankruptcy and paint the USPS as an expensive failure so the public will accept having another valuable public resource sold off at fire sale prices to private interests.
Said a shorter way, what "makes sense" from the standpoint of the public makes no sense at all from the viewpoint of those who feed off the public.