The fulcrum changes on an oval skew which increases the chance of a catch. It does not on a flat skew. I’m guessing the oval skew is part of a set. If you don’t have a flat skew, let that be your next tool purchase.
I don't agree.
I have a variety of skew shaft shapes: Thompson skews that have a 180-deg radius on the bottom edge, a couple of oval skews, and skews with rectangular shapes. (these have very slightly radiused corners so they won't catch on the rest, especially cast iron rests with unrepaired scratches or dents. (BTW, JB Weld epoxy will nicely fill porosity or dents on a cast iron tool rest that can't easily be filed away. Never a problem with Robust rests with a hardened steel rod on top.)
I don't notice any difference between the control or function of any cross section shape for straight or tapered planing cuts. Once I set the bevel correctly on the wood to make a shaving, the shape of shaft of the skew doesn't matter since the clearance angle varies SO little.
I wrote about this briefly in message #12 in this thread:
Are you referring to designs like Robert Sorby’s?
https://robert-sorby.co.uk/product/oval-skew-chisel-809/
I had that one and didn’t like it.
For a contrarian opinion

: I have two of those and find them great for turning. I find them easy to control for planing cuts and shallow curves, not my 1st choice for deep "v" grooves or facing cuts, and definitely not peeling.
What I DON'T like is sharpening them, especially at a small included angle - it's a pain to get both sides even enough that it won't annoy me! It would be better if I used a skew jig such as for the...
Twisting a skew during the cut will change the fulcrum, sometimes quickly! However, the ONLY reason I know to twist the skew during a planing cut in progress is to adjust the point of cut on the edge - if it's getting too high on the edge (a little too close to the long point), twist the skew handle a tiny bit conterclockwise if planing from R to L (adjusting the clearance angle a tiny bit at the same time to keep the shaving depth the same), clockwise if planing from L to R. I've never seen this taught - most people do it without thinking) but I use it in lessons with beginners as a way to explain how they can adjust the cutting spot on edge.
This assumes planing the the long point up - using the long point down is also usefult at times. This video explains. It looks useful for other reasons as well.
View: https://www.youtube.com/watch?v=cADbgJYeN-k
As mentioned, I do find the oval skews more difficult to sharpen. I almost always sharpen skews by hand on a tool rest set to the angle I want, using an 8" 600 grit CBN wheel (wide wheels with "square" edges, not the radius-edged wheels.) The cutting edge of the skew must be kept precisely horizontal or there will be areas of discontinuity in the bevel. The oval skew is difficult to keep the the edge oriented properly when sharpening by hand since it it too easy to roll a bit on the rest and too hard to keep the orientation perfect when moving the edge a bit horizontaly to a new spot on the wheel. One of the Tormek jigs is perfect for holding the oval skew for sharpening, here using it with a Tormek bar but should work with the tool rest too:
Message #49 in this thread:
I like my ... oval skews. Tormek revised the fixture so it no longer works as well with the diamond parting tool.
I've sharpened the oval skews on the Tormek but never the diamond parting tools. For that I use the platform on the Wolverine. When I get a moment I plan to machine a jig to hold the tool perpendicular to the wheel. Sometimes I accidentally introduce a slight angle on the cutting edge and have to regrind.
But since I bought all the original jigs that Tormek had (back at the birth of Tormek, I think) and later bought a second (used) Tormek that came with more jigs...
Follow-up question. I presumed that one factor with “catches” was that I was turning too slow (say, 800 rpm for 2” spindle), but given the catches was fearful of goinghigher. Since now I see that it can cut even with hand turning, maybe LOWER RPM is a way to learn the precise control? Thoughts?
The low speed is great for learning control. As I mentioned, after the new student gets to the point where I turn on the lathe, I run it at the slowest possible speed at first, then very gradually increase it as they gain confidence. Once you have the tool control under control

)), the faster the speed the easier and smoother the cut. (For a given lateral motion, a faster speed removes tinier shavings since it's making more revolutions for the same distance the cutting edge moves.) I typically turn thin spindes wide open, close to 3000 rpm on my lathe. A high speed makes it easier to control the vibration of the thin spindle.
Larger spindles (3" in dia or so) or very long spindles (shovel handle size, etc) I use a slower speed.
BTW, another thing that helps with a smooth skew planing cut is to find the optimum edge angle. (What I'm calling the "edge angle" is the angle between the edge and the long axis if the skew, NOT the clearance angle of the bevel with the wood!) I start students with the edge angle at about 45 degrees. After some experience, experiment with everything between a horizontal edge (which will give a peeling cut) to a vertical edge (which won't cut at all!) I adjust the angle a lot to see what works the best with specific wood diameters and blanks.
Finally, one natural but problematic thing to do is change the edge angle unintentionally DURING the planing cut down the spindle. Until a student learns to always move the body and legs (keeping the skew firmly at the same angle), the tendency is to stand rigidly at the starting position and sweep the cut with the arms. This tends to move skew so in a way that changes the edge angle - it's almost like an arc but with the gyrations needed to keep the skew cutting! This can change the edge angle from the desired starting angle to nearly vertical at the end of the cut. I've seen this over and over - it can cause several problems.
The easiest way to avoid this is to use a variation of the "woodturners dance." Most people learn the woodturner's skew dance quickly, but I had one person who just couldn't get it, even with constant reminders.
I first demonstrate the movement with the lathe off then have them try. To set up the cut, I have the student hold the skew on the rest at the starting position of the cut (with the lathe off at first), then, for a R to L cut, without changing the grip, step to the left until the intended ending position is comfortable, then keeping the feet in place on the floor and the skew in place in the hands, bend the legs and body to move the arms and skew back to the starting position of the cut. During the cut, bend the legs and body smoothly to move the skew down the spindle without changing the skew angle on the wood. This prevents the sweeping arc which can cause problems at the end of the cut!
All this is FAR easier to show than write about! Most people "get it" in about 10 seconds. And only need a few reminders after that. I think this is important for planing with a skew, coves with the spindle gouge, and outside cuts on a vessel or bowl.
(Oops, this was far more than I intended to write!)
JKJ