Did you measure the offset on those wheels,or are you aware of what that is? With wrong offset some cars, car setups, car/wheel/tire combos will make the car vibrate because of how it rides on that bearing and what that does to the entire geometry. Complicated so I wont' explain here, but it's known in racing at least, where throwing off the offset (angle change) will make it either vibrate or simply eat the bearings. I think 100% will disagree with me here,but they spent months in the factory calculating those wheels, tires, offsets, geometry, bearings, etc. Noting is there by accident. Changing wheels tires always affects the ride by lot. I have never driven a car in my life that had better ride quality after changing those parameters.
That would explain the first 5 mile problem you had as roads mostly have something called crown. That's where many alignment problems come out as it affects the car's "dynamic setup". Maybe that road did not have crown for a while (happens) and you were fine for few minutes. Or it could have been bad wheel, but guys that balance it would know right away. They don't need to be perfect to balance them, but tires do need to be in good condition (even).
Or bad wheels. I would not rule that out. To me that car was best in stock wheels and unmolested.
I highly doubt that's what is happening in the OP's case, given what we already know about the JNC wheels he bought, and the obvious runout damage on one of them from the vid he posted.
But fundamentally you're 100% correct here.
In my experience, the biggest factors there really are the weight of the installed wheels and how much offset was changed from the stock values.
Offset could be explained as being the load centerline of a given wheel/tire combo, so even when changing wheel size and width radically, the less deviance from the stock offsets, the better for ride quality and OE-like characteristics. When installing wheels of much lower offset, you're also changing the 'leverage' the wheel/tire combo has on the suspension assembly in that corner, by moving the moment out further from the control arm. So that means a given 'bump' in the road experienced by that wheel will push around the suspension a lot more easily -same as using a longer prybar makes it easier to pry something open- which in turn overpowers the spring and shock much more readily in addition to adding wear/tear on bushings/balljoints etc. The bigger the change in offset, the more 'leverage' you're adding to the suspension.
Similarly, installing a heavier wheel and tire combo will add inertia and more force to every part of the stock suspension, which affects ride quality and suspension performance in a similar way. The opposite is also true, in that going to a lighter wheel and tire combo often improves
ride quality as well as suspension performance and steering feel, and a lot of OE wheels are heavy as hell so there's often plenty of room to improve there.
Some cars are more susceptible to the wheel bearing damage and other issues caused by going crazy with offset changes. Subarus in particular tend to eat wheel bearings if you're going much lower than +40 offsets in any given wheel and especially if you're adding larger & heavier wheels and adding more camber.
Toyotas IME tend to be much more resistant to this and while JZA80's are needing wheel bearings now that they're so much older, I haven't seen a JZA80 or similar vintage Lexus that had wheel bearing damage or wear that seemed to be accelerated significantly by wheel or suspension changes.
FWIW, the nicest riding Supra I've ever experienced had a long-discontinued 17in Brembo F40 BBK up front (dropped close to 10lbs a corner vs the stock front brakes) 17in TE37's wearing Michelin Pilot Sport tires, and KW Variant 3 coilovers.
Light wheels, lighter brakes, and a top shelf coilover and tire choice. That's a fundamental recipe for success in improving all aspects of suspension performance.