Great, so we agree that your previous comment asking I address "paid browsers" in particular was an unnecessary distraction.
> I have a very hard time seeing an ethical distinction between running some proprietary code on my machine to complete a task and running some proprietary code on a cloud server to complete a task
It's important to recognize that copyright is entirely artificial. Congress went "let's grant creators some monopolies on their work so that they can make money off of it", and then made up some arbitrary lines for what they did and did not have a monopoly over. There's no principled ethical distinction between what is on one side of the line and the other, it's just where congress drew the arbitrary line in the sand. It then (arguably) becomes unethical to do things on the illegal side of the line precisely because we as a society agreed to respect the laws that put them on the illegal side of the line so that creators can make money in a fair and level playing field.
Sometimes the lines in the sand were in fact quite problematic. Like the fact that the original phrasing meant that running a computer program would almost certainly violate that law. So whenever that comes up congress amends the exact details of the line... in the US in the case of computers carving out an exception in section 117 of the copyright act. It provides that (in part)
> it is not an infringement for the owner of a copy of a computer program to make or authorize the making of another copy or adaptation of that computer program provided:
> (1) that such a new copy or adaptation is created as an essential step in the utilization of the computer program in conjunction with a machine and that it is used in no other manner
and provides the restriction that
> Adaptations so prepared may be transferred only with the authorization of the copyright owner.
By my very much not a lawyer reading of the law, those are the relevant parts of the law, they allow things like local ad-blockers, they disallow a third party website which downloads content (acquiring ownership on a lawfully made copy), modifies it (valid under the first exception if that was a step in using the website) and distributes the adapted website to their users (illegal without permission).