Not sure about the Dreamcast but with the GameCube I noticed the latency between plugging in a new controller and having the system respond to it is practically instantaneous.
I strongly suspect, but do not know, that the slowness in USB enumeration is a software stack issue on the host side of things.
If you think about plugging a USB device into a desktop OS, the OS has to check security settings, find and load a driver for the device, etc.
But as far as the protocol itself is concerned but I don't see any intrinsic reason why enumeration can't be nearly instant, for something like a console that only needs to recognize a few possible devices, each with minimal drivers that can be preloaded.
If you think about plugging a USB device into a desktop OS, the OS has to check security settings, find and load a driver for the device, etc.
But as far as the protocol itself is concerned but I don't see any intrinsic reason why enumeration can't be nearly instant, for something like a console that only needs to recognize a few possible devices, each with minimal drivers that can be preloaded.