The GPU could do the equivalent of fprintf, if the concerned peripherals used only memory-mapped I/O an the IOMMU would be configured to allow the GPU to access directly those peripherals, without any involvement from the OS kernel that runs on the CPU.
This is the same as on the CPU, where the kernel can allow a user process to access directly a peripheral, without using system calls, by mapping that peripheral in the memory space of the user process.
In both cases the peripheral must be assigned exclusively to the GPU or the user process. What is lost by not using system calls is the ability to share the peripheral between multiple processes, but the performance for the exclusive user of the peripheral can be considerably increased. Of course, the complexity of the user process or GPU code is also increased, because it must include the equivalent of the kernel device driver for that peripheral.
This is the same as on the CPU, where the kernel can allow a user process to access directly a peripheral, without using system calls, by mapping that peripheral in the memory space of the user process.
In both cases the peripheral must be assigned exclusively to the GPU or the user process. What is lost by not using system calls is the ability to share the peripheral between multiple processes, but the performance for the exclusive user of the peripheral can be considerably increased. Of course, the complexity of the user process or GPU code is also increased, because it must include the equivalent of the kernel device driver for that peripheral.