Thanks for your answer.
We still need to clarify why this is happening.
Any USB controller shares its bandwidth among its ports, but should provide the full power of the USB specification to each port.
This isn’t mentioned in the Wikipedia article for USB, but Scott Mueller mentions it in Upgrading and Repairing PCs:
Root hubs and self-powered hubs (hubs connected to an AC adapter) provide a full 500mA of power to each USB port. Root hubs are the USB hubs on motherboards.
I guess this applies to USB 3.0 too, which should provide 5v/900mA to each port.
I checked this by connecting a SATA 3 SSD, an iPhone and a Keyboard and mouse to the USB ports on my Mac Mini: then checked the system profiler > Hardware > USB section and I could see that 900mA are available for the SSD, 500mA to the Keyboard, 500mA to the iPhone…
Connecting several USB drives to any computer can potentially bottleneck the ports (data-wise) if the USB ports are connected to a single USB controller. That is why some motherboards feature more than 1 USB controller, so that its USB ports may provide the fullest possible USB bandwidth.
Unfortunately, this is not the case with the Mac Pro 2013, which has a single USB controller for its 4 USB 3.0 ports. Any attached devices should get the full 900mA/5volt power but share the data bandwidth.
This is dealt with in this article:
Mac Pro 2013 diagram
According to this article, attaching 3 drives may slow them down, but should not prevent them from being detected.