No. Standard indemnity clauses in contracts, plus realities of current mass communications, judicial, regulatory and political practices, combine to let the abuse transpire as the normal course for a plurality of the visas.
HCL/Cognizant/Wipro/Tata/etc.: We offer an awesome IT work force for cheap.
Disney/American-company: Great. Of course, by this contract you accept full responsibility for making sure everything you do is legal.
HCL/Cognizant/Wipro/Tata/etc.: Naturally.
Reality steps in at this point. Various visas can be abused in the transaction. Unless there is national media attention like in this case, there is no pressure on the transaction to curb the abuses. The body shops don't care if one or a handful of citizens successfully complain and overturn their individual positions; these outsourcing+offshoring contracts are typically huge, and a few positions out of hundreds will not tank the deal. Even if abuse is uncovered (and lacking specific facts in even Disney's case, there is no telling if what happened actually would run afoul of any regulations), there are no interested parties with sufficiently deep pockets to judicially prosecute. Even if it was successfully prosecuted judicially, the fines are a slap on the wrist for the big body shops. Even if the case is big enough that the judiciary kicks over the case to the relevant executive agency(ies) for follow up, there is no incentive for the agency to enforce the regulations; the body shops are their biggest "customers". Diminishing volume by banning or restricting to a "sit up and take notice" level like 5% of historical grants, increases the agency's work load per granted visa. It is less effort for the agency to process fewer grants of big blocks of visas, so the big body shops are attractive grant targets for the federal agency's management. Even if the agency's management makes an exception to make its life harder for itself and decides to take action, its life doesn't just become operationally more difficult, but also politically, which can result in budget cuts in retaliation and rebound into more operational challenges.
The incentives are quite stacked against individual American workers without access to equivalent collectivized resources that corporations and syndicates have. This won't change until the cost of living in the US comes way down. The low-hanging fruit for US cost of living is real estate (not the buildings, the dirt), as that comprises a minimum of 30% of wages, and in expensive tech metro areas, closer to 50% of wages. That isn't likely to happen short of massive macroeconomic changes, so that is why I don't think this situation will change in the near to mid-term (4-5 decades) future, if ever.
I wonder if a Purchasing Power Parity (PPP)-based reciprocal visa exchange might help ameliorate the situation, at least for citizens who can work remotely. For X visas granted to a nation, that nation immediately grants X * PPP-factor resident visas with the same duration to a random lottery of Americans who sign up for it, with Americans displaced by an H1-B receiving priority. Make the identification of displaced workers by time not by job, to avoid companies gaming the system. If a company lays off a citizen within X time, and hires an H1-B into any position within the same time period, regardless of the H1-B's job position or geographic location, then that citizen is counted as displaced. If by PPP the median wage in the US is 10X over India, then for each H1-B granted India opens up 10 visas of the same duration for Americans by lottery (or give first dibs to anyone who is replaced by an H1-B). I don't see this really helping older American workers closer to retirement, but for the subset of the HN crowd who see a streamlined visa process to live in India while building out their MVP and getting revenue traction, taking the "living day-to-day" expenses portion of their seed funding and expanding it out 5-10X could be very attractive.