I do agree that both corporations and unions ought to be regulated by antitrust law.
Ultimately that results in the wages offered being determined by the underlying market forces of supply and demand that are far larger and more powerful than the efforts of any single party. And it is in society's best interest for wages to be determined by supply and demand and not some social agenda.
The only policy which provide zero sum benefits to corporations at the expense of workers is immigration. And that can be addressed by workers through political coordination. The primary purpose of unions is to give select groups of workers the ability to engage in rent-seeking at the expense of the wider economy. We can get political coordination between workers without resorting to unions and all the harm that comes along with them.
If the market consists of few actors, you get collusion to depress wages and opportunity (in tech you had https://pando.com/2014/03/22/revealed-apple-and-googles-wage...) but it exists across a number of industries. Your assertion assumes only good actors, which is not commensurate with reality.
This sort of collusion can also be addressed in a much more targeted way than creating laws that give workers who unionize control over major hiring decisions of their employer.
Unions in the private sector became much weaker over the last 40 years, but that was not due to the labor laws that empower unions being eased. It was due to the type of industries that unions are prone to form in (e.g. labor-intensive, high volume manufacturing) contracting in the US.
The laws that empower unions make the US inhospitable to key industries.
What's going to happen to the US electric car manufacturing industry if Tesla's workers unionize?
What's going to happen to Amazon's business units if they see massive unionization?
The consequences for a US-based operation when their work force unionizes is a major disincentive for investing in production in the US, and a major impediment to existing US-centred companies from expanding.