A physical token only authenticates itself as “something you have” if there’s no way to extract the key from it. In practice non-hardcore deployments usually have a backup procedure but in principle, if you want multiple tokens, they should have separate keys. What you’re asking in simplest form involves storing the key on a server where it can potentially spill in a server breach or the like. If the key protects something very valuable, that can be dangerous. If it’s for your old Reddit account, you might decide to do it anyway.
The knives are out.