Dear Godchild,
Payroll in India was once upon a time (before 10 - 15 years) considered to be part of Accounts Department. Those are the days when payroll was seen as a mere compliance function and also as finance/accounting function as money was involved. Performance appraisal was more a ritual done once in a year and performance was not adequately related to pay. Moreover, Accounts personnel were the only people considered to be fit for doing statutory compliance realted jobs such as PF and ESI jobs in an organization.
In countries like US, even before 15 years Payroll was treated as part of the Compensation & Benefits Management, which is basically HR function. Payroll, as you can see, is only an event, which is happening at a frequency as may be stipulated by the country/company rules, and is guided by the policy on Compensation & Benefits Management program of any company. Other countries gradually adopted the concept.
Payroll is also a sensitive matter as employees may have queries when they receive their payslips. Not to generalise, Accounts personnel are not very much the right persons to have the kind of human relations skills to answer such queries with empathy and patience. So, Payroll also became a matter of human relations over years when employees mattered.
Another reason is the salaries have become more and more linked with employee performance and retention with a substantial part of salary paid as performance-linked incentive. Performance Management being the HR function, payroll management in a performance-oriented reward system has become HR function.
Accounts department mainly performs a control function and is therefore made as bottleneck. A bottleneck approach is not the right approach when you need to reward people's performace in a dynamic business environment. So, the payroll function has been transferred to HR to make it stay nearer to the people of the organization so as to respond quickly to the employees' queries and performance. Of course, Accounts will ultimately monitor the expenses and give their advice regarding any lapse in controls through audit and other tools.
If HR is not handling payroll with a difference and with what purpose it should handle this function, then it does not matter if Accounts handles it or HR handles it.
I think I have answered you to the extent I can. There could be different views/reasons to be put forth by other members.
Govardhan