"routinely assigned" is a correct and usable phrase in written English.
You can use it to describe a task or activity that is regularly given to or shared between multiple people. For example, "At the company, the administrative responsibilities were routinely assigned among the staff."
But later, she said in the complaint, she was routinely assigned to less desirable work stations.
Are the kinds of books routinely assigned for study in British universities now to be considered intrinsically suspicious?
Lawyers are now routinely assigned to them in court, and testimony guidelines help provide a safer, more comfortable environment, she said.
Even managers sent overseas by their companies are routinely assigned to back-office jobs until their superiors can be sure that their foreign ways have dissipated.
Routinely assigned to Casablanca by Warner Brothers in 1942, Epstein and his twin brother, Philip, never expected it to shake free of its chaotic creation.
Deputy mayors and other top city officials are routinely assigned cars and drivers, but it is not common for them to keep them once they leave.
The court routinely assigns a three-judge panel to hear each case.
That includes the performance of agencies like the Federal Bureau of Investigation, the Central Intelligence Agency and even the Social Security Administration, which routinely assigns Social Security numbers to foreigners who submit fake documents.
Other companies routinely assign specific people the responsibility of ensuring that decisions get turned into action; those people are held accountable for reporting on results at a meeting with executives.
Others say bosses would routinely assign extra tasks outside normal hours, leading many employees to procrastinate all day since they knew they had to stay late regardless of workload.
Most thriller writers aspire above the humble station that the literary world routinely assigns them — especially if their books have been critically welcomed, as Rabb's have been.
