can subwoofers make things worse?

I have two REL T/5x subs I just purchased. I also have a small listening space (12x9 or something close to that). They were easy to integrate and they make everything sound so much better. Soundstage, imaging, musicality, all better, not to mention the increased bass response that, I think, is outstanding. They are fast and tight which is the sound I was looking for. Integration is easy even though there is no app to help.  They connect at speaker level with Neutrik Speakon connectors which, I think, makes integration easy and matches the input to both speaker and sub.  I would highly recommend getting two. I love the RELs but others like the SVS and the KEF. The T/5x doesn’t go as low as the other two but I get very good in room response from them. Two of the RELs are about the price of the KEF as well.

I own the SVS Micro. That is your best bet.

Of course anything can make your sound worse if you don't know what you're doing

 But the SVS has a good Bluetooth app that lets you dial it in at your listening position

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.

I tried 5 different subwoofers, 4 of them made an absolute mess, also in a small room. It's very hard to get it right, if you have limited space and options. I am still better off when I turn off my sub.

Actually, a subwoofer can make things worse if it is incorrectly positioned in the room and/or bass traps are needed and not used, the wrong crossover frequency used, or the volume not correctly set.  For most setups this means a certainly amount of experimentation is required. However, once these issues are addressed, a sub can be a big plus in a system. 

However, even when the setup is done correctly, there can be a few situations where a sub will still makes things worse. That's where the recording itself has bass or sub-bass problems. I forget the exact recording, but I can think of one I heard a few years ago where the orchestra was apparently on a poorly constructed wood stand or floor and the sub did nothing but reveal a lot of very annoying thump-thump from foot stomping. 

I used a pair of REL T/Zero MKlll with Magnepan LRS+ in small room and sounded great...a poorly set up and integrated sub can certainly make things worse...

No, a sub will not make it worse… will likely enhance a good deal, two would be best.

REL… the default choice for most. High quality and great method and controls to feather it in with your speakers so not to create a mid bass hump.