The original idea with these sorts of things, at least in the US, is that we'd have administrative procedures and court adjudication to limit the harm that could come from that behavior. In practice, the administrative procedures are only a bar to the least knowledgeable plaintiffs, and the mere threat of litigation over a marginally valid claim is often enough to coerce most defendants into a settlement. Nobody wants to actually litigate whether or not a patent is obvious, or a copyright owner has been surreptitiously seeding their own works on BitTorrent.
There's also a question about whether or not your two examples are, in practice, always different cases. What if the person in the first example decides to not license their drug at all, so they can do the manufacturing themselves and control the price? That would be identical behavior to the second example... but they still made a useful invention. They're the same person.
You could legally restrict "non-practicing entities" from enforcing patent rights, but that's only a subset of all rent-seeking patent owners. Remember: the entire point of the system is to enable rent-seeking in lieu of up-front payments.
As in, allow entities to make a handsome profit, far outstripping their original investment. Just don't allow them to profit off of it forever. Patent and copyright expirations are a proxy for this, but they don't take into account the actual money & time invested, instead they replace them with a hard-coded magic number which will work for some products and fail for others.
In other words, once it becomes feasible to 'follow the money', it'll be somewhat trivial to see who's doing what and to what ends.
Notice that this problem doesn't exist in smaller communities, because everyone knows what everyone else is up to.
This is a data access problem that persists because it is profitable for people who have the power to keep everyone else in the dark regarding their machinations.
* Someone who literally figures out a new, cheap way to make a drug which cures a real disease
* Someone who, as soon as they get the right to, imposes license fees which serve no valid purpose, and profits in status & wealth from these new duties.