To me, these are some of them:
They can't open in your pocket and cut your hand when trying to reach them because they've inadvertedly open or the detent was weak. The sheath prevents that.
You can carry them in the pocket (small ones) without the clip showing, ripping your pants or the fabric, hitting and scratching things or bending. Can be worn in the neck if pockets are full or you have no pockets (Shower, swimsuit, pijamas...)
Better for food prep, cause the oils, sauces, food pieces, etc. are easily cleaned off and cannot get trapped inside pivots, locks etc. and rust them or block them. Easier to clean and mantain.
Stronger than folders for prying, stabbing or doing things in extreme angles, weird working positions etc. where a lock could fail or a pivot may break.
They beat folders for blade length/weight ratio almost every single time. Just try to get a 7" folding blade without having a pocket brick as a result. Handles can be skeletonised, also.
Some laws prohibit carrying folders but nothing against fixed blades. YMMV depending on where you live.
Easier to dismantle/take apart almost in every case.
If batoning or chopping needs arise, you have much less of a problem. Almost no parts that can get loose/break/etc.
No adjustments needed for blade centering/regular oiling in the pivot/lock engagement.