Subwoofer and 2 channel system - need to use crossover at all?

I love my Velodyne DD10 powered sub. (I have two, but one failed.  As others have said, a second does not make a big difference in a small or medium sized room).

My question is whether I should use a crossover at all with my 2-channel configuration.  Velodyne recommends running the signal lines from preamp to the sub, thereby using its crossover, and then running the remaining higher signal from the sub to the main speakers.  They say the sub plays the low signals "better" and relieves the main speakers from playing low frequencies, enabling better mid- and high- performance.  My preamp (Bryson PB25) has two sets of signal outputs, so I CAN send a full signal to the sub and to the floorstanding speakers - B&W Matrix 803 S2.  The B&Ws are rated down to 35hz and have 2 bass drivers each, but do not have deep bass like a good sub.  The B&Ws are overpowered - 600W monoblocks, so rationing amp power among the drivers is not an issue.  Currently I am running a full signal to both the B&Ws and to the sub and it sounds great.  I know that I can play around with the other configuration, but what does theory say?  In a 2 channel system without power constraints, should one allocate the low signal (at 60 or 80hz or whatever) exclusively to sub or let the floorstanding speakers and sub each have a full signal, and overlap output as they may?  Thanks