No, the real question is whether the framers intended to prohibit people from implicitly trading away certain individual rights in exchange for limiting what would otherwise be their unlimited personal liability.
Business activity was vastly different at the founding
They were aware of corporations as a business structure. English public stock corporations had played a major role in the founding of the colonies of Virginia (Virginia Company of London and Virginia Company of Plymouth) and Massachusetts (Massachusetts Bay Company), and also in the history of Canada (Hudson's Bay Company). They were certainly aware of these concepts. Corporations are older than the United States is.
That said, it was a much rarer business structure, only used for very large firms, because incorporating a company required a special act of Parliament – a power inherited by the colonial (and thereafter state) legislatures. It was not until the 19th century that it became the norm to for companies to be incorporated under a general incorporation statute, as opposed to a separate incorporation statute being passed to incorporate each individual company.
We don't get to label a group of citizens and then get to violate their rights because we labeled them.
"We" aren't labeling the citizens, they're doing so themselves. The default mode is that people are subject to unlimited personal liability for the harms they do to others. Society has chosen to make available a privilege of doing business in a limited-liability form (corporations, LLCs, LPs), but that privilege has strings attached. Don't like the strings? Then simply do business individually or as general partners — and accept the risk of unlimited personal liability.
(Also, the Seventh Amendment right to a jury trial applies to suits at common law; NLRB cases arise by statute, not common law, although SCOTUS has extended the jury right to so-called equivalents of common-law cases, which seems suspect.)
I swore an oath to defend that cloth multiple times and at this point it’s not clear that it holds up to 21st century scrutiny for being the kind of governing document we would create, should we have an opportunity to do so.
The Constitution is absolutely open to change via democratic means, but in absence of that, it is the democratic product of the people.
I wonder if the founders intended that the bill of rights be extended to legal entities?