Good points.
But you can add how HR can help reduce expenditure in the company-stationery, reduction in recruitment and training costs by selection of "best" candidate possible.
How HR can contribute to environment by reducing use of stationery and eco friendly materials in the running of office and admin functions of cafeteria, housekeeping etc.
Basically HR people should be thorough with latest laws/amendments.court rulings and beyond all that a genuine people frieindly person.
Emerging trends of Artificial Intelligence and use thereof in HR needs careful watch.
HR needs to ally with professional HODs and do Capability analytics which is a talent management process that allows you to identify the capabilities or core competencies you want and need in your business. Once you know what those capabilities are you can compare them to the capabilities you have in place at the moment to see if you have any gaps.
These capability gaps may put your company behind in a compettive environment.
Putting it in short
HR person should be alert to changes,updated in knowledge and ready to embrace changed ways of working with latest trends and technology.