This may be off topic because it is opinion-based and hypothetical in nature. There may be some merit however because it is presented with a "fair and impartial tone" and invites experiences over opinions that may be backed up with references. Especially in the world of coffee, where brewing methods are identified by brands, it is hard to not talk about specific products. Therefore, I'll try to answer as best I can.
First, let's talk about some of your suggestions:
Ideally, double-walled tempered glass housing
Part of the appeal of an Aeropress is that is durable, fool-proof, and easily brought on camping trips or stored in drawers and backpacks. Along with being bulky, doubled-walled glass or stainless steel would add weight and fragility.
fine stainless steel filter
This is definitely an option, and you can buy metal filters for a few popular brew methods including Chemex and Aeropress, and off course, french press is typically a metal mesh filter. The thing about metal filters compared to cloth or paper is that even the finest ones cannot filter at the same level. Metal filters will always let in more oils and fines compared to paper, and this is why the might not be desirable for an Aeropress, where clean, bright coffee is expected.
Is there any reason why cork wouldn't work for this?
Cork does seal well under the right conditions. But that's the key: right conditions. In a wine bottle, there is 1/2 and inch to 3/4 of an inch in diameter, and the cork is typically more than an inch long. It has also been created, molded, and formulated specifically for that task. A cork plunger would need to be thicker and be made specifically for that application to work, because you would't want it to flex and break the seal.
Also, cork is terrible at remaining taste-neutral. Every cup of coffee you brewed would impart taste into the cork and negatively effect every other cup. You could prevent this by putting a layer of something on the bottom if the cork, but then you start looking at using plastics.
If you're looking for brewing methods similar to the Aeropress, I might suggest something like the ROK. It uses hand pressure to extract espresso. No, i is not as easily carried around like an Aeropress but has a similar function.
If you're looking for brewers that have no plastic, well, there are many options in that field too such as french press, Chemex, mocha pot, espresso machine etc.
Beyond that, you could try modifying a glass french press with some sort of cloth filter to create a sort of reverse Aeropress. You can try looking around other options online too.
Hope this helps to answer your question!