Prostitution is institutionalised in Chinese culture and history, and socio-economic conditions in modern China make it an open secret.
There is even a saying to describe (male) vices: "吃喝嫖赌" (Eating, Drinking, Visiting Prostitutes, Gambling)
Contrast this with the European version:
Who does not love wine, women, and song
Remains a fool his whole life long.
The women here are, at the very least, not explicitly labelled as prostitutes.
History of Prostitution in China
There're various accounts of early prostitution in China but all seem to agree that it started as a state-sponsored enterprise, with government-run prostitution peaking during the Tang and Song dynasties. It seems prostitution was a part of life:
During the golden eras of Chinese literary history (Tang and Song dynasties), almost every great poet or politician mentioned his visits to prostitutes without any shame. It is not an exaggeration to claim that prostitutes played a role in stimulating some of the best poems in Chinese history.
(Source 2)
Of the 49,000 poems in 全唐诗 (The Complete Poetry of the Tang), "over 4,000 are related to prostitutes and 136 were written by prostitutes themselves" (The World of Chinese).
Marco Polo claimed that Peking had more than 20,000 prostitutes, and that there were so many in Hangzhou he could not give an estimate.
State prostitution continued until the Qing dynasty, when the Shunzhi and Kangxi Emperors wound down the local and Imperial governments' involvement in prostitution. However private prostitution continued. Prostitution was never legally sanctioned until the Republic of China was established in 1911.
In 1920 Shanghai, the
Shanghai Municipal Council calculated that more than 70,000 prostitutes were in the foreign concessions... If these figures are approximately correct, then in the French Concession in 1920, where there were 39,210 female adults on the population registers, one in every three women was a whore (Sun Guoqun 1988:-4). Altogether, it was estimated at the time that Shanghai's ratio of one prostitute to every 157 inhabitants was the highest among major world cities; Tokyo's ratio being 1:277; Chicago’s, 1:457; Paris’s, 1:481; Berlin’s, 1:582; and London’s, 1:906 (Yang Jjiezeng and He Wannan 1988:1).
(Source 3)
In conclusion, there is a long history in China of official attitudes to prostitution ranging from tolerance to active state involvement.
On the other hand, the People's Republic of China is intensely against prostitution, and cracked down on it soon after its establishment in 1949. As OP notes, it has not been successful.
Factors contributing to modern prostitution (and its acceptance)
On top of Chinese history, modern China also has many features which lead to prostitution being popular. Not all of these factors are explicitly linked to prostitution being open or acceptable, but I would argue that ubiquity tends to normalise an activity.
Sexual Attitudes of Chinese Women
Chinese women (like East Asian women in general [Source 6]) are sexually conservative, so Chinese men "resort to prostitution for their sexual demand"; where women are more free with their sexual favours, men are less likely to pay for them. For example, a 1992 survey found that 33% of men in the US who turned 20 in the 1950s had paid for sex, but thanks to the sexual revolution and women's lib, in the 1990s the rate dropped to as low as 5% (The University of Chicago Magazine: October 2002).
Sexual Repression
China is also a sexually repressed society. For instance, adultery got one a jail sentence until 1980 (Inside China’s Mistress-Industrial Complex).
There is also a concept of "性罪错" (Sexual Misconduct):
Castration, on the other hand, was traditionally reserved specifically for sex crimes. The Great Commentary to the Exalted Documents (Shang-shu ta-chuan 尚书大传， attributed to Fu Sheng 伏胜, fl. third—second centuries B.C.), for example, states that castration (kung 宮) is the punishment for “those men and women who have intercourse without morality” 男女不以義交者. One of the oldest explanations of kung comes in the Comprehensive Discussions in the White Tiger Hall (Po-hu t’ung 白虎堂), which explain that kung is the punishment for yin 淫, i.e., “licentiousness” or “promiscuity.”
女子淫，执置宫中， 不得出也。 丈夫淫， 割去其势也
When a woman is licentious, she is to be seized and held inside a room, and not allowed to leave. When a man is licentious, his genitals are to be cut off
(Source 5)
(I find this bit puzzling given how open China historically was about prostitution - perhaps someone else can shed light on it)
At one point premarital sex was officially grounds for expulsion at all Chinese universities (Chinese universities may alter tough sex rules) and at one sex between men and women was labelled prostitution (Guangdong college says all student sex is 'illegal prostitution', threatens expulsion).
An instructive comparison can be made with another, nearby East Asian country - Japan. Japan is a highly repressed society, and it is theorised that the popularity, ubiquity and outlandishness (or perversion, if you prefer) of Japanese pornography (JAV) stems from this repression.
Materialism and Income Inequality
The materialism and income inequality of modern China also contribute to prostitution's popularity.
The phenomenon of materialism is much discussed, and was neatly epitomised in a (female) contestant on China's most popular dating show proclaiming that "I'd rather cry in a BMW car than laugh on the backseat of a bicycle" (Page on time.com).
Meanwhile inequality meanss that, especially for rural women in the cities, prostitution is a rational choice:
The postsocialist traffic in women has given unprecedented commercial value to the nubile bodies of rural women who come to the city seeking work. As many of them quickly learn, it is hardly worth it to take a respectable but low-paying job as a maid when the likelihood of rape by an employer is so high. One young bar hostess put it this way: “Dalian men try to cheat both our bodies and emotions. Without spending a cent, they get what they want from us.” The only way to avoid being “tricked, used, and abandoned,” said another, is to protect yourself by making sure you get enough money for the sex you sell to men (Zheng 2009:220)... bar hostesses in the post-Mao era present themselves primarily as filial daughters serving their parents. They see doing sex work as a rational choice: it earns the highest return on the capital they have to invest (Zheng 2009:147-171).
(Source 4)
A close parallel to the openness of prostitution in China is its mistress culture, which is similarly widespread and open (Inside China’s Mistress-Industrial Complex), and whose concurrent popularity (and openess) spring from similar reasons.
One Child Policy
The one child policy has led to a shortage of women in China and
By 2030, projections suggest that more than 25% of Chinese men in their late 30s will never have married
(Why Chinese men are the most single in the world: the perils of gender imbalance in China)
Naturally, if there are many men who cannot find wives, the demand for prostitution will go up.
Even a Chinese official who advises the state on population issues has noted that an uptick in prostitution is an inevitable consequence of the One Child Policy (40m bachelors and no women ... the birth of a new problem for China).
Corruption
Corruption is widespread in China, and it is easy to bribe officials to turn a blind eye (Prostitution is Key to Reducing Corruption in China). Some are even actively paid by the sex industry.
Indeed, sex is part of the currency of corruption in China, with officials being "paid" with sex (Double standards on prostitution enrages blogosphere | Asia | DW.DE | 20.02.2014).
With such vested interests by many levels of government (and the promise of a quick buck by closing two eyes), it's no wonder prostitution persists.
(Long Format) Sources:
1) Sex in China: Studies in Sexology in Chinese Culture / Fang Fu Ruan
2) China's Policies toward Illegal Drugs and Prostitution in the New Era: Struggle within the Global Context / Bin Liang, Liqun Cao in Modern Chinese Legal Reform: New Perspectives / ed Xiaobing Li, Qiang Fang
3) Licensing Leisure: The Chinese Nationalists' Attempt to Regulate Shanghai, 1927-49 / Frederic Wakeman, Jr.
4) Gender and Sexuality in Modern Chinese History / Susan L. Mann
5) The Culture of Sex in Ancient China / Paul Rakita Goldin
6) Acculturation and sexual function in Asian women.
The Female Sexual Function Index (FSFI): development of a Japanese version.
Medscape Log In
The role of sex guilt in the relationship between culture and women's sexual desire.