can subwoofers make things worse?

That video was interesting and captured the fundamental difference in subwoofer approaches.  While I generally avoid subwoofers, I have helped with installations using them and I agree that REL is good at integrating the woofer with the main system (both effective and easy to accomplish). 
I have also heard SWARM subwoofers integrate well (not surprising because they employ many subwoofers to distribute room nodes).

The quality of sound with or without a subwoofer is a matter of both execution and personal preference.  Even in very rooms, with unlimited budget and no placement limitations, some people prefer not having subwoofers.  I usually prefer not having a subwoofer because I do not prioritize having ultra deep bass and prefer "fast" and clear sounding bass that is well integrated with the rest of the sound  i also don't want the temptation to fiddle with the bass balance for different recordings.  A local dealer who makes custom speaker systems refuses to utilize subwoofers.  Even in some systems he makes with twin 18" woofers per channel, the bass response is flat to just 35 hz or so because other aspects than ultra deep bass are being prioritized.