"The idea of patents is to reward inventors for their effort (and sharing the research results with others) by granting a monopoly so that they can use a shortage to drive up the price. "
Actually that's NOT the case and a company using a patent in this manner can (and frequently did) have it stripped, or forced to license in fair/equitable manners - which is what all the hallaballoo around 3G/4G/5G patent licensing is about when so many patents and crosspatent licensing is involved - some trolls keep on trying to submarine stuff into standards (RAMBUS) and then lay claim to it outside the FRAND frameworks.
Patents/Copyrights are SUPPOSED to ensure that an inventor/author gets a fair reward for the work done and protection for a SHORT period in exchange for putting that work into public domain. The fact that they've been weaponised as a way of keeping things OUT of public domain for extended periods shows how badly warped the system has become.
300-odd years ago, King James abolished the entire Royal Exclusive Patent system because of exactly the same kinds of abuses being seen now. It was only reinstated some years later when the abusers were nailed down (sometimes literally)