Neither did their European counterparts,IIRC.
I wouldn't say the Chinese government was powerless, but my point was that the Chinese state had fewer 'tools' at its disposal than contemporary W European nations to enforce its will, especially on issues such as patents and censorship.
The bureaucracy was not the only way Western European monarchs enforced public policy during this period - they also did it through commercial guilds and corporations. These organizations, which more often than not had state-sanctioned monopolies, brought the commercial interests of merchants in line with the political interests of the state, which meant that not only were merchants
not opposing the state, more often than not they willingly did the state's bidding.
To use the censorship example again: in China, if a book was to be banned, the task of doing just that would fall onto the bureaucracy. The bureaucracy would then lean on commercial publishers to stop printing copies. This is, to say the least, a daunting task, especially considering it is rarely in the commercial interest of any publisher to print less books (especially banned books), and so the bureaucracy would have had to act as monitor, judge and punisher all at the same time, with all the inefficiencies that would result.
Conversely in England, if a book was to be banned, the bureaucrats would instead lean on the Stationers' Company, which had a state-sanctioned monopoly over the English publishing industry, to enforce its laws. While it was of course in the Stationers' Company's interest to have its members print more books, it was even more important for the Company itself to maintain its monopoly. So rather than having to do the job themselves, English bureaucrats could conduct censorship with the help of the Stationers' Company and the publishing industry under it, which OTL did happen.
Back to patent enforcement. Like censorship, there will always be commercial incentive for individuals to violate patents, and it's beyond the capability of any pre-modern bureaucracy to monitor them all. National, state-sanctioned organizations relieve the bureaucracy of this burden by incentivizing private industries to comply with state laws or risk losing lucrative monopolies. It would have been impossible for the Chinese state to enforce a patent on, say, woodblock printing; it would be less of a stretch to imagine some hypothetical Chinese Printers' Guild enforcing patent on such things.
So would the Chinese state have been able to develop this sort of national guild organization through which patents can be enforced? Certainly guilds existed in China and in some cases, especially in terms of the Canton
hongs, the imperial Chinese state sanctioned their monopoly to achieve political ends. However, by and large Chinese guilds were both local in nature and also largely unacknowledged by the central government (perhaps because of their local-ness), and one could probably assume that Chinese Emperors would not have wanted a national guild organization that could compete with it in terms of power and prestige.