I have tripods with both 3 segments and 4 segments. A 4-segment tripod has 3 clamps per leg, which means 9 of them to open and close in extending and collapsing the tripod. That’s a pain. Enough of one that you sometimes find yourself asking whether a shot is worth setting up the tripod. But even 3 segment tripods are only a bit better.
I have my 4-segment legs because I can pack the tripod down into a reasonably small suitcase. I do most shooting when I travel so this is actually my best carbon fiber tripod. But when I am out carrying the tripod, or more commonly carrying it in the car, it doesn’t need to be this short. Unfortunately, the tripod fully extended, with camera and pano mount on it, is too long to fit in most cars, so I have to collapse one set of legs. That’s not so hard but it’s still very long and unweildy with just one set collapsed.
Here’s a possible answer: A 4 segment tripod where the bottom two segments join not with an external clamp, but which screw or snap together to make a smooth double-length segment. You used to be able to get monopods like this. Of course, the threaded join is not very convenient, and is not adjustable. However, you could readily take it apart to pack the tripod in a suitcase. If it can be made strong enough, a snap-together join would be best, with some recessed buttons to push to pull the legs apart. Then takedown and setup could be quick enough that you would also use it to put the pod into a backpack.
However, what you would have when put together is a 2-segment tripod, because the lower pair of segments, with no bumpy clamp, could feed up into the upper two segments when both of those are extended. In other words, you would have a nice tripod you could quickly reduce to half its length and back with just 3 clamps. A reasonable length for carrying and a very easy length to put into a car trunk or back seat.
You would not, however, be able to make the tripod any shorter than half-length without undoing the bottom join. Then you could get the tripod down to 1/4 length for low shots and for placing on tables and stone walls if half-length was just too high. That use is rare enough that I could handle that, especially if it’s just snaps.
The same approach could apply to your center column, or you could have just a 1/4 length center column, which is fine for most applications, since you don’t want to extend the column unless you have to, normally.
Note that the top join would be normal, so you would have 2 clamps per leg, and one hard-join. You don’t want a hard join at the top because presumably that will thin the inner diameter of the pole if you want it strong, stopping the lower segment from telescoping inside.
The 3rd segment (2nd from the ground) into which the bottom segment snaps, could also possibly have a spike or small foot coming out the center, which goes into a hole in the bottom segment. Or a place to attach such a foot. This would allow you to also configure a shorter, 3-segment standard tripod when you don’t want to snap in the lowest segment.