The phrase "grown more important" is correct and can be used in written English.
It means that something has become more significant or impactful over time. Example: "In recent years, sustainability has grown more important in consumers' minds, leading to a shift in their purchasing habits towards eco-friendly products."
Its voice has become increasingly influential as cash crops have grown more important to the Brazilian economy.
First, rating agencies' work on the risks inherent among issuers has grown more important as the corporate bond market has exploded in size.
As broadband has become more widespread — some governments want to turn it into a universal service like electricity or water — the quality of connections has grown more important.
The Parliament has since grown more important, with members periodically doing their best to embarrass cabinet members in the finest tradition of democratic rule.
As Chomsky has become increasingly alienated from the mainstream, though, his role in the American political debate has grown more important, not less.
Although the adoption of French, Italian, and other Western loanwords began in the early years of the Ottoman Empire, European vocabulary has grown more important in modern times.
"Maybe the hearth of the evening news will grow more important," Heyward says.
Then, with increasing leisure time for readers to both play and watch, sports grew more important to life and lifestyle.
As the trading function grew more important, those who remained craftsmen fell into a condition of dependence upon the traders.
A rosy view, perhaps, but as governments find themselves increasingly strapped for cash, intelligent giving can only grow more important.
In our global economy, the ability to understand languages other than one's native tongue grows more important every day.
