can subwoofers make things worse?

Subwoofers? We don't need no stinkin' subwoofers.

I have two 12" subs designed specifically for music by Rythmik and GR Research. In a very resolving system with full range speakers (mine play down to 26Hz before gently rolling off) you will find that some recordings sound much better with the subs and some sound worse. It's because of how different each recording emits bass. Most of my 60's and 70's rock recordings are deficient in bass and love added sub woofer with the crossovers turned fairly high. But the occasional excellent production/mastering/mixing/quality media recording suffer from the added bass. If a person were willing to dial in the sub for each recording it could work great but I find it best just to turn them off for really good recordings. Otherwise they just blur detail. All of this assumes the subs are setup correctly.

Bottom line, I think your stand mounts with limited low end would love a sub but a full range speaker with highly resolving system can be hit and miss. Still worth having though. Oh, and I would recommend considering Rhythmic with the custom audio grade driver by GR Research. They use servo technology unique from other servo units and sell direct so the bang for buck is serious.

Short answer: "Yes". If you reside in a multi-family dwelling, a subwoofer can make the relationship with your adjacent neighbors worse.

+1 @wolf_garcia Explains what I mentioned as sound stage expansion.

Rel T series don't move air and shake room, roll off bass in lowest registers. As others have mentioned neighbors can be a very real concern, I was the one calling police on a very careless neighbor! So, not wanting to bother my neighbors was a major concern when purchasing  these subs, I stood outside my house and not really much more boom than my Klipschorns without subs. Subs with lower reach and capable of much greater output will have much greater chance of bothering neighbors. My Genesis sub moves air and shakes room, makes it unusable in my situation.

Sub placement will be key in a small room.  Try to locate the sub(s) anywhere but in-between the main speakers.