When I was new to this, yes the wobbly unipivots (ala VPI) were unsettling. But this was misplaced nerves. Now - it’s no big deal! Use the cueing lever / lift. Of course, it doesn’t feel like a good idea to put a stiffly suspensioned, massy cartridge (Koetsu) on one of these. But for most MCs and MM it works fine.
There are many offshoots of the "pure" unipivot - usually by adding additional pivots of some sort (which is a broad canvas). I’d consider these more of a hybrid. The aforementioned Graham Phantom uses the magnetic stabilization, which works quite well and handles much like a traditional gimbal arm. Phantoms also do well with Koetsus, which seem to appreciate the enhanced stability.
VPIs can add the "dual pivot" mod. Though I’m not sure how well that "swash pad" bearing holds up over time. At least it’s easy enough to replace. I liked VPI’s metal unipivots - late builds of these wands were great, IMO. Really nice build quality and "feel". I had much more issues with the 3D and Fatboy wands. Very reactive to bass frequencies in my setup (~ 100Hz). I think it was more a matter of the wand material, than the unipivot bearing itself - but that could have played a factor too. I know the 3D / Fatboys are generally more popular than metal in this ecosystem - but not for me.