The phrase "responsibility of providing" is grammatically correct and can be used in written English.
It is commonly used to describe the duty or obligation of a person or organization to supply or offer something. Example: As the head of the department, it is my responsibility of providing the necessary resources for our team to complete the project on time.
He made it clear that a variety of mechanisms would be used to provide all Californians with insurance and that the responsibility of providing it would fall on the government, employers, health care providers and the uninsured themselves.
State accepted the responsibility of providing inexpensive higher education at the undergraduate, graduate, and professional levels.
Healthcare professionals have the responsibility of providing breastfeeding education to families.
As the eldest son in the family, he took on the responsibility of providing for the family.
The inevitability of psychological crises does nothing to absolve us of the responsibility of providing that care.
Some drivers have asked for lease extensions or offered to buy the cars and release G.M. from the responsibility of providing parts or service.
The responsibility of providing access often falls to the development community, but is enough being done to turn access into knowledge, and knowledge into power?
He had taken on the responsibility of providing a plain white image for the cameras to use for color balancing, something done before every news conference.
For example, during the period of the Soviet Union's existence in the 20th century, the government was charged with the responsibility of providing health care to all citizens.
An outstanding feature of his existence was his ability to attract the goodwill of patrons prepared to relieve him of the responsibility of providing for his livelihood.
In the late Roman Empire most praetorships disappeared, but the praetor urbanus remained, with the responsibility of providing the public games.
