The phrase 'become varied' is grammatically correct and can be used in written English.
For example, you could use it in a sentence such as "As I got older, my interests became varied."
With the high fashion interest, menswear pants designs have become varied; from the typical suit pants (with no pleat, one pleat, and two pleats on the front) to casual pants (denim pants, cargo pants, baggy pants, and sports pants, etc).
So when people are forced to cover a story after the fact, quite naturally the accounts of the accident have become varied, from "He just broke his nose and one of his cheek bones" to "they had to reattach his nose".
Once metastatic disease develops, practices become varied.
That way, you will become varied in the types of houses to display.
In the process, central banks have become varied in authority, autonomy, functions, and instruments of action.
The fast growth of technology and its impact on all production industry has enabled computer-generated animation techniques to become varied and widespread.
It wasn't until after the Second World War, with the arrival of American food aid as well as new fishing and storage technologies, that Japanese cuisine became varied in both seasoning and substance.
Genre and subject matter have become more varied too.
Christian yoga and yoga on the go in a new room at the San Francisco International Airport are proof that the practice of this meditative activity has become increasingly varied.
During the past 15 years, evidence for an ice-rich planet Mars has rapidly mounted, become increasingly varied in terms of types of deposits and types of observational data, and has become more widespread across the surface.
There's a new buzz-word in the world of DJing: "Button Pushers". As the DJ moves from club booths to festival stages, the equipment has become increasingly varied.
