You're correct that British made factory goods would have been good for China, specifically the Chinese poor, as it would have enabled them to have many low quality goods rather than a few higher quality goods.
The issue is that when you present goods like mass produced clay teapots, cotton textiles, etc to the customs agents of the country which invented fine china, and silk, you're not going to impress them.
And yes, Britain coveted China. As did Japan, Russia, Germany, The United States, France, Italy, and Austria-Hungary. Even after they won the opium wars and got their favorable trades, they continued to work to overthrow or minimize the Qing dynasty and take political power. The Qing ended up sputtering out a few years before it became unfashionable to be a colonialist, so China dissolved into rule by warlords, then conquered by Japan, then the communists won and the rest is history.
