I could explain all the basic models of vibrating systems, string under tension, stiff rods and plates with boundary conditions, air columns, etc. But I am not sure that would answer you question. For one thing one of your basic statements is simply not true (and I think you suspected it).
"With singing I generally understand that changes by step are easier to perform than leaps, or at least so I've heard. Perhaps that isn't really true?"
This depends on so many factors, some of which may be psychological or slight physiological differences among humans. For example, I am a natural "leaper" as my vocal coach says. She (my coach) is more able to sing scale melodies (and always has been), yet I can jump up a tower of 4ths or 5ths easily (within range of course).
There are two potential interpretations of the qualifier "Easy". If you mean easy to hear in your head then this may not have anything to do with physics. On the other hand if you mean easy on the throat + diaphragm + sinus system then some of it may have to do with physics but also physiology (which one could argue can be modeled with physics). In a nut shell we need to be able to hear where we want to go, and be able to adjust our body to go there. These "two minds" in a sense need to be in sync.
The amazing thing about singing is that you don't really need to change anything consciously to change pitch, even though something is changing. What I mean is that you don't need to consciously squeeze or tighten anything in your neck or throat to change pitch, if you do you will likely hurt yourself. With some training you should be able to slide (siren) up and down scales and arpeggios smoothly. The real issue is will you "stop" at the right places. If you have a hard time being in tune then you just need ear training and practice. But if you have real physical problems getting good tone etc then this is physical and would likely be the result of not have a good support from the diaphragm, running out of air, etc. Again, not a problem with vocal fold tension or anything like that, but an air flow problem.
Most people have a "transition" note where one can feel the resonance in the head more pronounced. At this point it becomes physically more difficult to move smoothly up and down the scale near the transition note. However, once you are out of that region it becomes easy again. Being in tune is not so much the problem as having a shaky sounding voice, almost like a pre-teen whose voice is changing and cracking. It is common to feel the resonance of lower pitch notes in the chest and higher pitch notes in the head but in fact all notes are resonating through the entire column. With training one learns to feel head resonance without cutting off the chest resonance and vice verse. This provides the proper support for those transition notes.
I do not believe that larger jumps would naturally be harder to get accurately as the previous answer states. In my case, first day of lessons I could nail large jumps. To the point about being able to hear the target note better, past exposure to those intervals helps (it gives you a mental frame of reference). Since I've played guitar (and violin) for 40+ years I can hear the tower of 4ths (one 3rd) and 5ths in my sleep. So in a sense I have those intervals memorized. While the muscles do have to increase tension I do not think this is the reason why some intervals may seem more or less difficult to hit in general.
Another thing to consider in your question is not whether a 5th is easier than (or harder than) a half step but whether the situation changes in different octaves. At the low end of our range (especially if you are a bass) you may not even be able to hear or feel the difference between two notes a half step apart, while a fifth may be easy. 2 or 3 octaves higher the situation may flip.