You might be more inclined to appreciate the sound of flats on your own bass if you appreciated the sound of flats on someone else's bass.
Starting playing bass well after the heyday of flatwound strings, what drew me to try them was hearing this tone on 1960s/1970s records, like Joe Osborn and Carol Kaye. I didn't even know what role the strings played, but I liked that sound, and I knew that I wasn't getting that sound.
It wasn't until I tried flatwound strings that I got that sound (or at least in the ballpark). And then I ran with flatwound strings a lot for years.
I wouldn't say that I grew tired of them, as I still love the sound, but I have since then realized that most of the music I personally play is better suited by roundwound strings, and drifted back to mostly using rounds again. (Have used GHS Pressurewounds a lot also.)
I did find that some flats agreed with my personal taste more than others. I came to really super like the tone of Rotosound 77 flatwound strings, but have mixed feelings about their stiffness and slightly lower output. I like GHS flats, probably about tied with the Rotosounds overall. I like Labella DTF, but am not super into Labella LTF. I like the TI flats, but found them maybe a bit TOO flexible, and I didn't like how the E string lacked low-end depth. Etc. There are differences even amongst flats, and you might have to try more than one kind to get the tone you want.
That is, if you want flatwound tone at all! If you don't hear flatwound strings on records and think "wow, I want to sound like that!" then maybe flatwound strings aren't for you.
