"universal adoption" is correct and usable in written English.
You can use it when you want to refer to the acceptance and implementation of something by a majority or across a wide area. For example, "Universal adoption of the new law would help bring peace to the region."
But progress toward universal adoption has been slow.
(Living Goods has solved these problems, but is still short of its goal of universal adoption).
The most important innovation was the rapid and almost universal adoption by bank customers of electronic bill payments.
The only barrier to its universal adoption is the high cost of equipment: an average of forty thousand dollars a machine.
The New Yorker, December 30 , 1939P. 21 PROFILE of Elisabeth Achelis who has, since 1930, spent practically all her time trying to secure the universal adoption of a permanent, unchanging calendar.
One independent candidate bugged by a voguish euphemism is Ralph Nader, who called me the other day to register a complaint about the unthinking, universal adoption of the word detainee.
These advances, together with the almost universal adoption of radial-ply construction (described below), have extended the life expectancy of some tires to more than 90,000 miles (150,000 km).
Will key states without nuclear weapons support universal adoption of the stronger International Atomic Energy Agency inspection protocols necessary to build everyone's confidence that proliferation will not occur as nuclear energy technology spreads to new markets?
With almost universal adoption of EIA, projects are increasingly subject to more than one assessment process.
Facebook though, has achieved near universal adoption in the United States.
"What if the browser, with near universal adoption, could become the keystone of an open, interoperable communications system".
