I think flat desktop cases might not be a bad answer, especially with the useless stands that come on most monitors these days with no height adjustment. Typically I need to raise a monitor several inches to not have to tilt it up and stare down at it, which is terrible posture. Going back to the old style (CRT sitting on top of a beefy steel desktop box) wouldn't be so bad.
Otherwise, even without an industry standardized max-length, enthusiast case manufacturers could solve this by providing their own brackets that span the width of the case and screw onto matching holes across from the PCI-e mounts. They could even put RGB lights on them to make them look less ugly for people with glass side panels.
You can mount the card vertically with a riser cable. It won't solve the problem of it taking up all slots but it won't risk sagging either.
My card (an ASRock 6900XT, 332mm, 1.78kg per reviews) came with a bracket that's a modestly beefy-looking piece of steel, but it just bolts into two or three more thumbscrew sockets, and the actual contact-point with the card is a glued on rubber bumper that's like 2mm x 15mm and a rubber bumper, so there's opportunity for it to bend or not align with the card well, and the bumper gets unglued, and it blocks all your slots.
I ended up getting the type of bracket that's a rod with a little magnetic foot to anchor it to the bottom of the case, and then another foot that the card rests on. Again, this is dependent on how tightly the thumbscrew holds the top foot in place, but hopefully the downward force from the card is being projected straight down the bracket.
The right answer is probably to reintroduce flat-mount 'desktop style' cases. There was zero sag risk when I had the build in a CoolerMaster HAF-XB, but it was a bit shallow for a card that big - you couldn't get the card out without disassembling everything and lifting at odd angles while applying enough force to rip the clip off the end of the PCI-E slot.
Alternatively, if we could get some collaboration in the industry, they could agree on a standard "max length". I note there are some documents suggesting the maximum length for an ISA or PCI card used to be ~338mm. In that scenario, the cases can be designed with an explicit assumption there will be a 338mm card installed, and there are little support rails at the front to engage a card of about 338mm long. These could help bear the load and ensure the card remained aligned.
Ancient PCs had this-- I can recall opening an old Compaq 286 and seeing it stuffed full of "full length" cards neatly fitting into rails in the case. Back then, the cases were desktop and the cards were light, so the rails were more for management and neatness, but there's no reason they couldn't carry weight in a modern revision.
I think I've also seen it with some weird OEM builds more recently-- they'll add a metal or plastic shim to the front of a long card so it matches up with rails in the one case it was designed to fit into.