With stud grade stuff, I might agree to a point. Carefully thought out and well built however, wood benches can be remarkably strong. With "good wood" however, it might be cheaper to buy a welder and steel, and a week long welding class......
Lesser woods, even right down to stud grade can still be remarkably stout. It just puts the onus on you to make sure that the overall thing is built well, joints fit well, flats line up. Bolted or screwed, you'll still want well fitting joints. Glue, (again, done with care and strategy) in any joints that are going to be "tested" in normal use, be it for supporting weight or resisting racking or whatever....
I've got this project on my "medium term" radar. My bench will be wood, not because I "have to", not because I "need to", not because it's "better", but because I enjoy such things, and it's what I want. And because it will be the way I want (mostly), it's not going to be as stout as I could make it. Way more so than steel of the same weight. Nowhere close to as stout as steel of the same volume. But it will be at the point where the returns (in my world) won't be tangible.
1.) Wood does contract and expand. If the overall assembly is made of the same wood not over constrained, maintains some degree of geometrical symmetry in it's structural components, it won't be trememdous. Or it will, but it'll be symmetrical. The frame you have pictured, all the "lumber" that makes up the bulk of the bench, that won't bother you at all. Wood expands on it's width (across the grain) much moreso than it does lengthwise. And even if it did expand an unacceptable amount lengthwise, the symmetry says that it's' going to stay as level as your floor does. (Put a pin in that......)
The really big problem might be with the top. If the top were made of lumber, as I "might" do anyhow, because it is "managable", if not solvable, the movement of the top of the bench would be your biggest issue, compared to the whole rest of the frame. If the top is made of plywood, if you bullzeye all the screws at the center of all the framing members you have pictured, you could screw, glue, and generally lock it down hard, and it won't bother. Plywood's expansion and contraction is minimal (often considered zero), and in practice is a pretty good match for the expansion lengthwise (with the grain) on the frame.
The legs of that stand, somewhere you said 4X4 lumber for that? That's hard (and by that I mean "expensive") to find that without a heart in it. It's probably gonna twist on you.... It probably won't matter to the leveling situation, and if it does, once it "goes", and you correct for it, it probably won't bother again. The biggist thing that really means in building a bench is "have a plan and get it done". A week or two versus months or longer. Once it's all screwed/glued/bolted together, it'll stay better, move less, and it'll all move together, which means as long as you don't have the metrology tools out, it'll be fine.
2.) Sealing is not really required. The wood will soak up oils and fluids and all for sure. It won't hurt it, except that you'll never be able to "clean it off" to look like new. And chips aren't so easy to brush off of it. I've got a wood (plywood) top on the "big" workbench at work, and also my "mechanic's cart" is made (well made.....) with common white pine boards. Both of those have been thorougly finished in carb cleaner and used oil finish over the years. They look greasy and oily, but just like wood with "proper" oil finishes, the boss can take his office job clean hands and move my cart around, or do things on the work bench. It doesn't track.
If you were to seal it, paint or otherwise, my strong recommendation would be to do all or nothing. Either way, it WILL acclimate to the ambient humidity, but if you seal it, you slow the process. If you slow some places, and not others, then you get differential movements.
For the sides and back, I'd highly agree with you that panels would do well. Just like the top, they could be anything, but I'd recommend plywood there as well. As fancy or as crude as you choose to be, it can be made to work well. Or "real wood" can work too, again, if you choose to take on the art of managing the seasonal changes. Mine won't be that, that part if mine is gonna be plywood.
With the back and sides done, instead of sandbags inside the bottom, I'd think the better approach would be a pair of hinged doors in the front, or drawers (built, bought, scavenged, whatever, and load it up with tools, materials, etc.
Don't get "too" excited about torsion boxes. The ones you see on youtube are increadible, however to accomplish that they are using a high amount of engineering, an increadible degree of accuracy in their cutting, and they're universally using materials that are 100 percent dimensionally consistant in three dimensions. To do the same with lumber, the way it was done before somebody gave it a name, and for a bench that's gonna be less than three feet deep... The way it was done is pretty much what you see in the drawing you posted. Good square cuts on all the pieces, cross members well attached, the top attached well to all of the framing and cross members.... You're pretty much there. You could get some (probably not tangible but absolutely real) gains from another layer on the underside off the top framing, but my thoughts are this- You'd get MORE benefit from taking that extra chunk of plywood and doubling the top . Screwed on a grid (for clamping mostly) and the two glued together, Stronger bolting for the lathe, solid enough to do work on, (you can HAMMER on a regular shop work bench built this way). Not that there's anything wrong with the torsion boxes anyone is building, it's just that unless you're doing something that is HUGE in size, or needs to be able to stand on three legs, good old run of the mill utility benches (well built) aren't that far from the mark.
How will you attach wooden end caps to the end grain? Door shims under a leg work very well..... Seriously, while I'm half way joking about the door shims, the end grain situation is hard to make go away. My solution is going to be shims (maybe or maybe not door shims, but shims nonetheless), as this is not something that needs to be done every day. And in practice, only access to the front legs are needed. It won't move enough to require such drastic adjustments at all. I'm not 100 percent sure, barring any changes in my master plan, this is not this summer's thing, but the following one. Plans could change. But I believe, I am going to leave ONE front leg about a quarter inch short, and use two tapered "somethings" to make one solid parallel adjustable shim. (Kind of like a door shim, but maybe a better material). The initial bench leveling can literally be done in place during construction, as close as it can reasonably be, and literally finished with a hand plane until my metrology department is exhausted, before the top is in place. Beyond that, level doesn't really bother me so much as "twist. That can be adjusted either way at that single point.
My solution for mobility is going to be based on constructing the lower "shelf" so that it can be accessed and lifted from two sides and one end with a pallet jack. Or more likely it'll be set up to properly "catch" a pallet truck from for all four sides, but I think center of mass issues might prevent lifting from one end. So I kind of sidestepped casters/endgrain issue. If I were confined to the bench being on it's own wheels, I'd probably be inclined, depending on how the final bench works out,to make the lower shelf framework coincide with the bottom of the legs, so that it could be available at three sides of the caster for support. That means the fourth hole (in the leg end grain), would only ever see pressure loads, the screw would be there on principal, but it'd never get "tested" in real use. But don't discount other ideas over that, it's not a new problem, and I'm sure there's a slew of ways, in various degrees of cleverness, expedience, expense, etc. That's just what comes to mind right off.