The phrase "becoming increasingly important to" is a correct and usable phrase in written English. You can use it when describing the increasing importance of something, such as a particular topic or activity. For example, "Environmental protection is becoming increasingly important to governments around the world.".
As the history of annotation changes becomes larger and more complex, it is becoming increasingly important to facilitate complex searching of updates.
That dynamic is becoming increasingly important to the music industry".
The cloud is becoming increasingly important to Oracle.
Netflix's international expansion is becoming increasingly important to the company's growth plans.
But it's becoming increasingly important to ask hard questions about value for money.
It is against this backdrop that the region is becoming increasingly important to European universities.
"Now it is becoming increasingly important to their economic well-being as well".
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia