Like when the rental company only has a Yaris, when you have a reservation for a Midsize. Or when your own SUV (I've always had 30+/37+ US/UK-mpg 4-cylinder eco-SUVs) breaks down, and you're in the same boat, getting the only rental car available (often Yaris-land).
As far as "shock," that what inserting foam under the base and around the unit is for. Furthermore, the products usually come with cardboard inserts that fit the stick to perfection. The rudder isn't usually an issue after putting foam under the base. If they cannot take excessive shock beyond that, they wouldn't have survived in the original box.
Only when flying or shipping do I get something like you suggest, and I'm shipping thousands upon thousands of dollars of equipment (if not $10K+).
I had a SATA connector break off when I've checked an even double-boxed computer in as luggage. I know what they go through! So that's when one (1) big case makes sense, and form-fitted. In fact, when travelling overseas, I only take one (1) roller of clothes and fit everything in it. I can always rewash after 10-12 days (so many hotels offer such and it's worth it). Not worth having more luggage misplaced or stolen.
You don't know what idiots are going to be throwing your boxes around, and where they might go. So yes, those hardened, rated cases with custom cut, foam inserts are worth the price. That's why I've paid for them -- lugged them around and paid
the massive cost of shipping those heavy suckers -- when I'm shipping computers (even Mini-ITX and Nano-ITX systems) and other, delicate equipment to my clients. In fact, those "costs" often become an issue, which is why I have to repeat to them,
"This is why I quote training almost $5,000 cheaper if you provide your own labs. The shipping can add up to $1,000-1,500 alone, and that's not including the other logistics that cost me both upfront and continuing."But when driving ... the plastic totes are just fine.
Many come very water resistant, even when "poured" all over the top of them, continually (some even rated NEMA 3). Some are even available with gaskets if you want to pay more. I don't see the need. I'm not going to be immersing them in water, or ... reality check ... I'm going to be paying for water damage in my car.
I.e., the HOTAS is the last thing on my mind, let alone going to get damaged only after it's really bad in my trunk!
As always, I don't suggest anything I haven't personally, and even professionally, done. This is not rocket science (although I have done some 6DoF integrals in that regard too), but someone wanting to move around a US$200 HOTAS, not thousands of dollars of equipment. YMMV, but this is mine.
I've been 100% travel for over 10 of the last 15 years. Those little, plastic totes do the job very nicely when driving all across the USA for me (yes, I've even done 2,400mi/4,000km straight). As I said, I even put my Mini-ITX computers themselves in a plastic tote. And I did a lot of training and carried a full classroom of systems at one point. They do the job, and nicely, when they go in a car.
Personally, I think this is overkill. Unless you can find a big, used, waterproof box and an uncut insert for $50 that you can customize, it's not worth it. I mean, you're going to start taking up 3-4x the volume. Understand I say this as someone who has designed embedded systems for outdoor use too. It's overkill for this app in my experience. But YMMV.
SIDE NOTE: I also don't put all my camera gear in one bag any more. E.g., I had someone try to "help me" by "throwing" my sling bag over their shoulder like it was a "backpack," when I purposely told them to not touch it. It suddenly left their shoulder like it they shotput it, destroying $2,000 of camera gear. Sometimes having more than one bag has its benefits, like someone only destroying one or two things, instead of a half-dozen. Just an added consideration. 
) so the Hotas X looks like a good idea 
